a likelihood ratio test for stationarity of rating transitions abstract we study the time stationarity of rating transitions modelled by a time continuous discrete state markov process and derive a likelihood ratio test for multiple markov processes from a multiplicative intensity model maximum likelihood parameter estimates can be written as martingale transform of the processes counting transitions between the rating states so that the profile partial likelihood ratio is asymptotically 2 distributed an application to an internal rating data set reveals highly significant instationarity

cauchy like and pellet like results for polynomials abstract we obtain several cauchy like and pellet like results for the zeros of a general complex polynomial by considering similarity transformations of the squared companion matrix and by treating the zeros of a scalar polynomial as the eigenvalues of a matrix polynomial

stability of reducing subspaces abstract we characterize the stability of reducing subspaces of a rectangular matrix pencil of complex matrices b a except for the special case in which the pencil has no eigenvalues and only has one row and one column minimal indices and both are different from zero

statistical tests for multivariate bioequivalence although the u s food and drug administration fda 1992 recommends testing bioequivalence of individual pharmacokinetic parameters one at a time it seems reasonable and interesting to conduct a test simultaneously for all the parameters in this paper we discuss several ways to construct such tests it is shown that the confidence set approach leads to a test which can be uniformly improved by the intersection of schuirmann s two one sided tests procedure the latter test can further be improved upon noticeably by using the one dimensional unbiased test of brown hwang munk 1997 numerical calculations of powers are given to support this claim

about boundary values in a omega assume that c n is a balanced bounded domain with a holomorphic support function e g strictly pseudoconvex domain with c 2 boundary we denote f 2 z 1 0 f e 2 it z 2 dt let e 0 and be a circular invariant borel probability measure on if g a and h is a continuous function on with g h on then we construct nonconstant functions f 1 f 2 a with g f 1 z h z g f 2 z max 1 h z for z and additionally if is a circular bounded strictly convex domain with c 2 boundary then we give the construction of f 3 o the holomorphic function with h g f 3 z 0 for all z where f denotes the radial limit of f we also construct f 4 a with g f 4 z h z for z in all cases we can make f i arbitrarily small on a given compact subset f c and make it vanish to a given order at the point 0

simultaneous confidence regions for multivariate bioequivalence demonstrating bioequivalence of several pharmacokinetic pk parameters such as auc and cmax that are calculated from the same biological sample measurements is in fact a multivariate problem even though this is neglected by most practitioners and regulatory bodies who typically settle for separate univariate analyses we believe however that a truly multivariate evaluation of all pk measures simultaneously is clearly more adequate in this paper we review methods to construct joint confidence regions around multivariate normal means and investigate their usefulness in simultaneous bioequivalence problems via simulation some of them work well for idealised scenarios but break down when faced with real data challenges such as unknown variance and correlation among the pk parameters we study the shapes of the confidence regions resulting from different methods discuss how marginal simultaneous confidence intervals for the individual pk measures can be derived and illustrate the application to data from a trial on ticlopidine hydrochloride an r package is available

inverse spectral problems for differential pencils on the half line with turning points the inverse spectral problem of recovering pencils of second order differential operators on the half line with turning points is studied we establish properties of the spectral characteristics give a formulation of the inverse problem prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem

log majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots we show that the sequence of moduli of the eigenvalues of a matrix polynomial is log majorized up to universal constants by a sequence of tropical roots depending only on the norms of the matrix coefficients these tropical roots are the non differentiability points of an auxiliary tropical polynomial or equivalently the opposites of the slopes of its newton polygon this extends to the case of matrix polynomials some bounds obtained by hadamard ostrowski and pa lya for the roots of scalar polynomials we also obtain new bounds in the scalar case which are accurate for fewnomials or when the tropical roots are well separated

algorithms for hyperbolic quadratic eigenvalue problems we consider the quadratic eigenvalue problem or the qep 2 a b c x 0 where a b and c are hermitian with a positive definite the qep is called hyperbolic if x bx 2 4 x ax x cx for all nonzero x c r we show that a relatively efficient test for hyperbolicity can be obtained by computing the eigenvalues of the qep a hyperbolic qep is overdamped if b is positive definite and c is positive semidefinite we show that a hyperbolic qep whose eigenvalues are necessarily real is overdamped if and only if its largest eigenvalue is nonpositive for overdamped qeps we show that all eigenpairs can be found efficiently by finding two solutions of the corresponding quadratic matrix equation using a method based on cyclic reduction we also present a new measure for the degree of hyperbolicity of a hyperbolic qep

structured backward error analysis for sparse polynomial eigenvalue problems abstract we study a backward error analysis for structured polynomial eigenvalue problems in homogeneous form arising in practical applications the perturbation matrices preserve the sparsity as well as other structures including symmetry skew symmetry hermite skew hermite we construct structured perturbation matrices of minimal frobenius norm such that an approximate eigenpair is an exact eigenpair of the structured perturbed polynomial eigenvalue problem this work is a complement of previous work for the polynomial eigenvalue problems in homogeneous form

the block numerical range of matrix polynomials block numerical ranges of matrix polynomials especially the quadratic numerical range are considered the main results concern spectral inclusion boundedness of the block numerical range an estimate of the resolvent in terms of the quadratic numerical range geometrical properties of the quadratic numerical range and inclusion between block numerical ranges of the matrix polynomials for refined block decompositions as an application we connect the quadratic numerical range with the localization of the spectrum of matrix polynomials

assessment of individual and population bioequivalence using the probability that bioavailabilities are similar in this paper a new method for the assessment of both individual and population bioequivalence is proposed that is derived from the approach of schall and luus 1993 statistics in medicine 12 1109 1124 the method considers the probability that the bioavailability of the test product is close to the bioavailability of the reference product against the probability that the bioavailability of the reference product is close to itself when administered on different occasions the method can accommodate unequal variances of the bioavailabilities of the test and reference formulations as well as formulation by subject interaction it is thus as general and comprehensive as the methods proposed by sheiner 1992 statistics in medicine 11 1777 1778 and schall and luus 1993 but the resulting bioequivalence criteria are simple and easy to interpret

confidence intervals associated with tests for bioequivalence summary previously the connection between bioequivalence tests and their associated confidence intervals was not well understood in fact the oc level two one sided tests approach was thought to be associated with a 1 20c confidence interval in this paper we build up connections which allow us to construct 1 oc confidence intervals from cx level tests and vice versa when applied to the cc level two one sided tests the resultant 1 oc confidence intervals are properly contained in westlake s 1 oc symmetric interval 1976 our approach is readily generalized to different settings including the nonparametric setting the ratio parameter setting and the repeated confidence interval setting

bayesian modeling of multivariate average bioequivalence bioequivalence trials are usually conducted to compare two or more formulations of a drug simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence despite the fact that some tests for multivariate bioequivalence are suggested current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as auc and cmax in this paper we develop a semiparametric bayesian test for bioequivalence under multiple endpoints specifically we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference resulting estimates and posterior probabilities borrow strength from one another where the amount and the direction of the strength borrowed are determined by the prior correlations the method developed is illustrated using a real data set copyright 2007 john wiley sons ltd

sample sizes for bioequivalence studies in recent years a number of decision rules based on sound statistical principles have been proposed for deciding if a test formulation is bioequivalent to a reference formulation the decision rule based on confidence intervals has been accepted by regulatory agencies at least by the food and drug administration of the united states a useful property of this decision rule is that the regulatory agency need not require a certain sample size since the level of protection against wrongly deciding bioequivalence is set by the choice of the alpha level used to compute the confidence intervals the manufacturer claiming bioequivalence is concerned about sample size for sample size determines the probability of falsely deciding non bioequivalence when the test formulation does indeed have an acceptable relative bioavailability curves of probability of rejecting bioequivalence have been computed for error coefficient of variation of 10 20 and 30 per cent for relative bioavailability from 70 to 130 per cent and for protection levels of 90 and 95 per cent these curves can be used for choosing the sample size for a bioequivalence study

localization theorems for nonlinear eigenvalue problems let t omega rightarrow mathbb c n times n be a matrix valued function that is analytic on some simply connected domain omega subset mathbb c a point lambda in omega is an eigenvalue if the matrix t lambda is singular in this article we describe new localization results for nonlinear eigenvalue problems that generalize gershgorin s theorem pseudospectral inclusion theorems and the bauer fike theorem we use our results to analyze three nonlinear eigenvalue problems an example from delay differential equations a problem due to hadeler and a quantum resonance computation

first order spectral perturbation theory of square singular matrix pencils abstract let h a 0 a 1 be a square singular matrix pencil and let 0 c be an eventually multiple eigenvalue of h it is known that arbitrarily small perturbations of h can move the eigenvalues of h anywhere in the complex plane i e the eigenvalues are discontinuous functions of the entries of a 0 and a 1 therefore it is not possible to develop an eigenvalue perturbation theory for arbitrary perturbations of h however if the perturbations are restricted to lie in an appropriate set then the eigenvalues change continuously we prove that this set of perturbations is generic i e it contains almost all pencils and present sufficient conditions for a pencil to be in this set in addition for perturbations in this set explicit first order perturbation expansions of 0 are obtained in terms of the perturbation pencil and bases of the left and right null spaces of h 0 both for simple and multiple eigenvalues infinite eigenvalues are also considered finally information on the eigenvectors of the generically regular perturbed pencil is presented we obtain as corollaries results for regular pencils that are also new

some large scale matrix computation problems abstract there are numerous applications in physics statistics and electrical circuit simulation where it is required to bound entries and the trace of the inverse and the determinant of a large sparse matrix all these computational tasks are related to the central mathematical problem studied in this paper namely bounding the bilinear form u t f a v for a given matrix a and vectors u and v where f is a given smooth function and is defined on the spectrum of a we will study a practical numerical algorithm for bounding the bilinear form where the matrix a is only referenced through matrix vector multiplications a monte carlo method is also presented to efficiently estimate the trace of the inverse and the determinant of a large sparse matrix

constrained simultaneous confidence intervals for multiple comparisons with the best for comparing k treatment effects 01 02 ok often the parameters of primary interest are 0i maxeioi0 i 1 k in this article we develop constrained 100p two sided simultaneous confidence intervals for 0i maxj i0j which we refer to as constrained mcb intervals it turns out that the lower bounds of the intervals imply indifference zone selection inference and the upper bounds of these intervals imply subset selection inference each given at the same confidence level 100p as mcb we also extend our

bounds for eigenvalues of matrix polynomials with applications to scalar polynomials abstract we first generalize to complex matrix polynomials an improvement of an upper bound by cauchy on the zeros of complex scalar polynomials the bound requires the unique positive root of a real scalar polynomial of the same degree as the given complex scalar or matrix polynomial we then create a recursive procedure to represent a matrix polynomial by another matrix polynomial of larger size but of lower degree we apply this procedure to scalar polynomials and then apply the generalized improved cauchy bound to their matrix polynomial representation often obtaining a better bound by solving a real scalar polynomial equation of significantly reduced degree

nonscalar matrix polynomial representation of some scalar polynomials abstract we show how a class of scalar polynomials can be expressed as nonscalar matrix polynomials to which matrix methods can be applied that yield improvements over scalar results and generate new ones to demonstrate the advantages of this approach we use it to compute bounds for the zeros of those polynomials

semiparametric bayesian modeling of multivariate average bioequivalence bioequivalence trials are usually conducted to compare two or more formulations of a drug simultaneous assessment of bioequivalence on multiple endpoints is called multivariate bioequivalence despite the fact that some tests for multivariate bioequivalence are suggested current practice usually involves univariate bioequivalence assessments ignoring the correlations between the endpoints such as auc and cmax in this paper we develop a semiparametric bayesian test for bioequivalence under multiple endpoints specifically we show how the correlation between the endpoints can be incorporated in the analysis and how this correlation affects the inference resulting estimates and posterior probabilities borrow strength from one another where the amount and direction of the strength borrowed are deter department of mathematics and statistics georgia state university atlanta ga 30303 3083 usa email pghosh mathstat gsu edu department of epidemiology and biostatistics memorial sloan kettering cancer center 1275 york avenue new york ny 10021

stability criteria of matrix polynomials abstractin this paper the stability of matrix polynomials is investigated first upper and lower bounds are derived for the eigenvalues of a matrix polynomial the bounds are based on the spectra

an improvement of commonly used tests in bioequivalence assessment if equivalence of two treatments has to be proved by an experiment with normally distributed observations and fixed sample size there are two usual methods on the one hand there is the double t test and on the other hand a test procedure suggested by anderson hauck which is uniformly more powerful than the first one but only capable of keeping asymptotically to the nominal level based on these two methods a new test is presented which is uniformly more powerful than the double t test and also keeps the preassigned level

a unifying approach for confidence intervals and testing of equivalence and difference summary general families of null hypotheses are defined which refer to problems of testing equivalence and difference between treatments corresponding confidence intervals have been proposed in the literature in a different context the unifying approach demonstrates how waiving of particular one sided tests in the parameter space relates to the construction of the corresponding confidence interval

asymptotic representations for root vectors of nonselfadjoint operators and pencils generated by an aircraft wing model in subsonic air flow this paper is the second in a series of several works devoted to the asymptotic and spectral analysis of an aircraft wing in a subsonic air flow this model has been developed in the flight systems research center of ucla and is presented in the works by a v balakrishnan the model is governed by a system of two coupled integrodifferential equations and a two parameter family of boundary conditions modeling the action of the self straining actuators the differential parts of the above equations form a coupled linear hyperbolic system the integral parts are of the convolution type the system of equations of motion is equivalent to a single operator evolution convolution equation in the energy space the laplace transform of the solution of this equation can be represented in terms of the so called generalized resolvent operator which is an operator valued function of the spectral parameter this generalized resolvent operator is a finite meromorphic function on the complex plane having the branch cut along the negative real semi axis its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces in the first paper and in the present one our main object of interest is the dynamics generator of the differential parts of the system it is a nonselfadjoint operator in the energy space with a purely discrete spectrum in the first paper we have shown that the spectrum consists of two branches and have derived their precise spectral asymptotics in the present paper we derive the asymptotical approximations for the mode shapes based on the asymptotical results of these first two papers in the next paper we will discuss the geometric properties of the mode shapes such as minimality completeness and the riesz basis property in the energy space

a construction of inner functions on the unit ball in c p in their recent paper 1 hakim and sibony came very close to constructing inner functions on the unit ball in c e in fact only some minor modifications of their arguments are necessary to produce bona fide inner functions the present paper carries out these modifications since we need to point out some information not explicitly stated but clear from the context in their paper and to make the exposition self contained we repeat most of the material in their paper our lemma 1 for instance is identical to their lemma 3 and our application of lemma 1 in the proof of lemma 2 is the same as theirs in the proof of theorem 1 the following notations are used b is the unit ball in c p br z cp izl r we use the distance

optimal confidence sets bioequivalence and the limacon of pascal abstract we begin with a decision theoretic investigation into confidence sets that minimize expected volume at a given parameter value such sets are constructed by inverting a family of uniformly most powerful tests and hence they also enjoy the optimality property of being uniformly most accurate in addition these sets possess bayesian optimal volume properties and represent the first case to our knowledge of a frequentist 1 confidence set that possesses a bayesian optimality property the hypothesis testing problem that generates these sets is similar to that encountered in bioequivalence testing our sets are optimal for testing bioequivalence in certain settings in the case of the normal distribution the optimal set is a curve known as the limacon of pascal we illustrate the use of these curves with a biopharmaceutical example

on lower and upper bounds in smooth and strongly convex optimization we develop a novel framework to study smooth and strongly convex optimization algorithms focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear operators this in turn reveals a powerful connection between a class of optimization algorithms and the analytic theory of polynomials whereby new lower and upper bounds are derived whereas existing lower bounds for this setting are only valid when the dimensionality scales with the number of iterations our lower bound holds in the natural regime where the dimensionality is fixed lastly expressing it as an optimal solution for the corresponding optimization problem over polynomials as formulated by our framework we present a novel systematic derivation of nesterov s well known accelerated gradient descent method this rather natural interpretation of agd contrasts with earlier ones which lacked a simple yet solid motivation

a peak set of hausdorff dimension 2n 1 for the algebra a in the boundary of a domain with c boundary in c ⁿ

1 α equivariant confidence rules for convex alternatives are α 2 level tests with applications to the multivariate assessment of bioequivalence abstract in general a 1 confidence region c x for a parameter yields a test at level a for h h versus k c h whenever we reject if c x h we show under certain equivariance properties of c x that for the case of convex alternatives c h the level of the resulting test is in fact 2 this extends recent findings for hyperrectangular alternatives as they occur in the multivariate bioequivalence problem furthermore we apply the suggested test to ellipsoid type alternatives instead of hyperrectangulars in the multivariate bioequivalence problem and to a problem occurring in neurophysiology finally we compare our test numerically with existing methods

an alternative to student s t test for problems with indifference zones consider a sample from a normal population with mean mu and variance unknown suppose it is desired to test h 0 mu leq mu 0 versus h 1 mu geq mu 1 with the region h i 1 mu 0 mu mu 1 being a nonempty indifference zone it is shown that the usual student s t test is inadmissible for this problem an alternative test is proposed the two sided problem with indifference region is also discussed by contrast with the above result the usual student s t test is admissible here however the two sided version of the alternative test mentioned above does offer some practical advantages relative to the two sided t test a 3 decision version of the two sided problem is also discussed here the t test is inadmissible and is dominated by the appropriate version of the alternative test the results concerning tests are also reformulated as results about confidence procedures

scaling sensitivity and stability in the numerical solution of quadratic eigenvalue problems the most common way of solving the quadratic eigenvalue problem qep l 2 m l d k x 0 is to convert it into a linear problem l x y z 0 of twice the dimension and solve the linear problem by the qz algorithm or a krylov method in doing so it is important to understand the influence of the linearization process on the accuracy and stability of the computed solution we discuss these issues for three particular linearizations the standard companion linearization and two linearizations that preserve symmetry in the problem for illustration we employ a model qep describing the motion of a beam simply supported at both ends and damped at the midpoint we show that the above linearizations lead to poor numerical results for the beam problem but that a two parameter scaling proposed by fan lin and van dooren cures the instabilities we also show that half of the eigenvalues of the beam qep are pure imaginary and are eigenvalues of the undamped problem our analysis makes use of recently developed theory explaining the sensitivity and stability of linearizations the main conclusions of which are summarized as well as arguing that scaling should routinely be used we give guidance on how to choose a linearization and illustrate the practical value of condition numbers and backward errors

iterative system solvers for the frequency analysis of linear mechanical systems abstract the paper deals with the numerical treatment of the direct frequency domain dfd analysis of linear mechanical systems attention is mainly focused on the solution of the complex system of equations needed for each analyzed frequency strategies for transforming the system into the shifted form t i z d are proposed and discussed where is related to the frequency for two formulations of the shifted system the performance of some krylov sub space iterative solvers is tested and compared to that of a multi frontal direct method advantage is taken of the shifted form in solving simultaneously a large number of systems resulting from different values of the shift frequency numerical experiments on some prototype structural dynamics problems are reported the results shown demonstrate how the devised strategies for the iterative solution can outperform in many cases the direct solver

carleson sobolev measures for weighted bloch spaces abstract carleson sobolev measures for weighted bloch spaces on the unit ball of c n are described the classical carleson measures for growth spaces on special circular domains are characterized

linear operator pencils on lie algebras and laurent biorthogonal polynomials we study operator pencils on generators of the lie algebras sl2 and the oscillator algebra these pencils are linear in a spectral parameter the corresponding generalized eigenvalue problem gives rise to some sets of orthogonal polynomials and laurent biorthogonal polynomials lbp expressed in terms of the gauss 2f1 and degenerate 1f1 hypergeometric functions for special choices of the parameters of the pencils we identify the resulting polynomials with the hendriksen van rossum lbp which are widely believed to be the biorthogonal analogues of the classical orthogonal polynomials this places these examples under the umbrella of the generalized bispectral problem which is considered here other non bispectral cases give rise to some nonclassical orthogonal polynomials including tricomi carlitz and random walk polynomials an application to solutions of relativistic toda chain is considered

sums of characteristic values of compact polynomial operator pencils we consider polynomial pencils whose coefficients are compact operators bounds for the sums of absolute values real and imaginary parts of characteristic values are derived applications to differential and difference equations are discussed

an unbiased test for the bioequivalence problem it is shown that the standard two one sided tests procedure for bioequivalence is a biased test better tests exist in this paper an unbiased level test and other tests which are uniformly more powerful than the two one sided tests procedure are constructed its power can be noticeably larger than that of the level two one sided tests procedure

directional bounds for polynomial zeros and eigenvalues abstract directional versions of theorems by cauchy and pellet are obtained for both scalar and matrix polynomials which derive bounds on the zeros of scalar polynomials and eigenvalues of matrix polynomials that depend on their arguments such bounds often deliver much better results than the standard theorems which are formulated in terms of the moduli of the zeros or eigenvalues only and are therefore insensitive to their arguments

more on pseudospectra for polynomial eigenvalue problems and applications in control theory definitions and characterizations of pseudospectra are given for rectangular matrix poly nomials expressed in homogeneous form p da d d 1 a d 1 da 0 it is shown that problems with infinite pseudo eigenvalues are elegantly treated in this framework for such problems stereographic projection onto the riemann sphere is shown to provide a convenient way to visualize pseudospectra lower bounds for the distance to the nearest nonregular polynomial and the nearest uncontrollable dth order system with equality for standard state space systems are obtained in terms of pseudospectra showing that pseudospectra are a fundamental tool for reasoning about matrix polynomials in areas such as control theory how and why to incorporate linear structure into pseudospectra is also discussed by example

complete proper holomorphic embeddings of strictly pseudoconvex domains into balls abstract we construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with c 2 boundary in c n into the unit ball of c n for n large enough thereby answering a question of alarcon and forstneric 2013

instability indices for matrix polynomials abstract there is a well established instability index theory for linear and quadratic matrix polynomials for which the coefficient matrices are hermitian and skew hermitian this theory relates the number of negative directions for the matrix coefficients which are hermitian to the total number of unstable eigenvalues for the polynomial herein we extend the theory to even matrix polynomials of any finite degree in particular unlike previously known cases we show that the instability index depends upon the size of the matrices when the degree of the polynomial is greater than two we also consider hermitian matrix polynomials and derive an index which counts the number of eigenvalues with nonpositive imaginary part the results are refined if we consider the hermitian matrix polynomial to be a perturbation of a even polynomials however this refinement requires additional assumptions on the matrix coefficients

bounds for characteristic values of entire matrix pencils entire matrix valued functions of a complex argument entire matrix pencils are considered upper bounds for sums of characteristic values and a lower bound for the smallest characteristic value are derived in the terms of the coefficients of the taylor series these results are new even for polynomial pencils

generalization and variations of pellet s theorem for matrix polynomials abstract we derive a generalized matrix version of pellet s theorem itself based on a generalized rouche theorem for matrix valued functions to generate upper lower and internal bounds on the eigenvalues of matrix polynomials variations of the theorem are suggested to try and overcome situations where pellet s theorem cannot be applied

bounds for eigenvalues of matrix polynomials upper and lower bounds are derived for the absolute values of the eigenvalues of a matrix polynomial or matrix the bounds are based on norms of the coefficient matrices and involve the inverses of the leading and trailing coefficient matrices they generalize various existing bounds for scalar polynomials and single matrices a variety of tools are used in the derivations including block companion matrices gershgorin s theorem the numerical radius and associated scalar polynomials numerical experiments show that the bounds can be surprisingly sharp on practical problems

a multivariate test for population bioequivalence in this article we propose a multivariate generalization of the criteria for testing univariate population bioequivalence recently a number of approaches for testing multivariate equivalence have appeared in the literature most of them consider a multivariate equivalence region which implies simultaneous comparison of means in each dimension in contrast our proposal combines a comparison of means and a comparison of variances into a single aggregate criterion using the trace of the covariance matrix as a scalar measure of the total variability we use a confidence interval approach to multivariate population bioequivalence testing similar to the univariate case two versions of the modified large sample confidence interval for the linearized multivariate criterion are constructed in a simulation study we evaluate the empirical coverage of these confidence intervals and rejection rates of the corresponding tests in finite samples the proposed methodology is illustrated with an example of testing equivalence of the spray pattern of nasal sprays

identities for sums of characteristic values of entire matrix pencils abstract the paper deals with an entire matrix valued function of a complex argument an entire matrix pencil f of order f identities for the following sums of the characteristic values z k f k 1 2 of f are established k 1 1 z k m f m f and k 1 im 1 z k f 2 f 2 the suggested results are new even for polynomial pencils

higher radial derivative of functions of qp spaces and its applications in this paper we give some characterizations of the integral and carleson type measure both associated with higher radial derivative for holomorphic functions of q p 0 and q p spaces in the unit ball of c n as applications some sharp forms of the relations between dirichlet type spaces and q p 0 spaces are shown by means of higher radial derivative carleson type measure and constructive methods for the cases of determinism and randomization respectively

empirical bayes confidence sets for the mean of a multivariate normal distribution abstract through the use of an empirical bayes argument a confidence set for the mean of a multivariate normal distribution is derived the set is a recentered sphere is easy to compute and has uniformly smaller volume than the usual confidence set an exact formula for the coverage probability is derived and numerical evidence is presented which shows that the empirical bayes set uniformly dominates the usual set in coverage probability

reverse estimates in growth spaces let h b d denote the space of holomorphic functions on the unit ball b d of mathbb c d given a radial doubling weight w we construct functions f g in h b 1 such that f g is comparable to w also we obtain similar results for b d d 2 and for circular strictly convex domains with smooth boundary as an application we study weighted composition operators and related integral operators on growth spaces of holomorphic functions

spaces m dp bnp and qp abstract in this paper the relations between d p and b n p m d p and b n p are discussed by means of high order radial derivative and random series the main results of this paper are 1 let i if 0 b n q d p ii if n p 2 q b n q and d p cannot included each other iii if q 3n p 2 then d p b n q 2 let 0 i if 0 b n q m d p ii if n p 2 q b n q and m d p cannot included each other iii if q 3n p 2 then m d p b n q 3 let n 1 n m d n 1 p q p

new bounds for roots of polynomials based on fiedler companion matrices abstract several matrix norms of the classical frobenius companion matrices of a monic polynomial p z have been used in the literature to obtain simple lower and upper bounds on the absolute values of the roots of p z recently m fiedler 2003 9 has introduced a new family of companion matrices of p z that has received considerable attention and it is natural to investigate if matrix norms of fiedler companion matrices may be used to obtain new and sharper lower and upper bounds on the development of such bounds requires first to know simple expressions for some relevant matrix norms of fiedler matrices and we obtain them in the case of the 1 and matrix norms with these expressions at hand we will show that norms of fiedler matrices produce many new bounds but that none of them improves significatively the classical bounds obtained from the frobenius companion matrices however we will prove that if the norms of the inverses of fiedler matrices are used then another family of new bounds on is obtained and some of the bounds in this family improve significatively the bounds coming from the frobenius companion matrices for certain polynomials

on the numerical solution of lambda 2 a lambda b c x b and application to structural dynamics in this paper we address the numerical solution of a large linear system depending quadratically on a parameter that varies in a wide range we analyze a solution method whose computational cost grows only sublinearly with the number of parameters that relies on the use of an indefinite inner product important implementation aspects are treated in detail the problem arises in various application areas we shall report on our experience with cases in structural dynamics

on uniformly bounded bases in spaces of holomorphic functions the main result of the paper is the construction of explicit uniformly bounded bases in the spaces of complex homogenous polynomials on the unit ball of c 3 extending an earlier result of the author in the c 2 case