invertibility of irreducible matrices abstract we obtain new sufficient conditions for invertibility of an irreducible complex matrix remarks are also given on eigenvalues and the associated eigenvectors that lie on the boundary of various spectrum inclusion regions of an irreducible matrix our results extend strengthen or clarify the recent work of brualdi brualdi and mellendorff farid solov ev and zhang and gu

brauer type eigenvalue inclusion sets of stochastic irreducible tensors and positive definiteness of tensors abstract in this paper brauer type eigenvalue inclusion sets of stochastic tensors and irreducible tensors are given respectively some sufficient conditions of positive semi definiteness of stochastic tensors are obtained furthermore the stability of a high order nonlinear system is analysed by positive definiteness of tensors

on schur complement of block diagonally dominant matrices abstract it is well known that the schur complements of strictly diagonally dominant matrices are strictly diagonally dominant d carlson t markham schur complements of diagonally dominant matrices czech math j 29 104 1979 246 251 the same is true of generalized strictly diagonally dominant matrices jianzhou liu yungqing huang some properties on schur complements of h matrix and diagonally dominant matrices linear algebra appl 389 2004 365 380 in this paper this result is extended to the block strictly diagonally dominant matrices and the generalized block strictly diagonally dominant matrices that is it is shown that the schur complement of a block strictly diagonally dominant matrix is a block strictly diagonally dominant matrix and so is the schur complement of a generalized block strictly diagonally dominant matrix

stability analysis of diagonally equipotent matrices diagonally equipotent matrices are diagonally dominant matrices for which dominance is never strict in any coordinate they appear e g as laplacian matrices of signed graphs we show in this paper that for this class of matrices it is possible to provide a complete characterization of the stability properties based only on the signs of the entries of the matrices

nonsingularity singularity criteria for nonstrictly block diagonally dominant matrices abstract let a a ij n i j 1 c n n be a block irreducible matrix with nonsingular diagonal blocks v v i c n be a positive vector and let n j 1 2pt j i a 1 ii a ij v j v i i 1 n under these assumptions necessary and sufficient conditions for a to be singular are obtained based on a block generalization of wielandt s lemma the pointwise case n n of irreducible matrices with nonstrict generalized diagonal dominance is treated separately for an irreducible matrix a conditions necessary and sufficient for a boundary point of the union of the gerschgorin s circles and of the union of the ovals of cassini to be an eigenvalue of a are derived

notes on matrices with diagonally dominant properties abstract in this paper we analyze the relation between some classes of matrices with variants of the diagonal dominance property we establish a sufficient condition for a generalized doubly diagonally dominant matrix to be invertible sufficient conditions for a matrix to be strictly generalized diagonally dominant are also presented we provide a sufficient condition for the invertibility of a cyclically diagonally dominant matrix these sufficient conditions do not assume the irreducibility of the matrix

a note on a brauer s theorem abstract let a be an n n irreducible matrix and be an eigenvalue of a we obtain some necessary and sufficient conditions for to be a boundary point of the cassini oval inclusion region of the eigenvalues of a these results correct a classical result of a brauer

the eigenvalue distribution on schur complements of h matrices abstract the paper studies the eigenvalue distribution of some special matrices tong in theorem 1 2 of wen ting tong on the distribution of eigenvalues of some matrices acta math sinica china 20 4 1977 273 275 gives conditions for an n n matrix a sdn idn to have j r a eigenvalues with positive real part and j r a eigenvalues with negative real part a counter example is given in this paper to show that the conditions of the theorem are not true a corrected condition is then proposed under which the conclusion of the theorem holds then the corrected condition is applied to establish some results about the eigenvalue distribution of the schur complements of h matrices with complex diagonal entries several conditions on the n n matrix a and the subset n 1 2 n are presented such that the schur complement matrix a of the matrix a has j r a j r a eigenvalues with positive real part and j r a j r a eigenvalues with negative real part

covariate adjustment of event histories estimated from markov chains the additive approach summary markov chain models are frequently used for studying event histories that include transitions between several states an empirical transition matrix for nonhomogeneous markov chains has previously been developed including a detailed statistical theory based on counting processes and martingales in this article we show how to estimate transition probabilities dependent on covariates this technique may e g be used for making estimates of individual prognosis in epidemiological or clinical studies the covariates are included through nonparametric additive models on the transition intensities of the markov chain the additive model allows for estimation of covariate dependent transition intensities and again a detailed theory exists based on counting processes the martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model resulting in estimates that can be expressed as stochastic integrals and hence their properties are easily evaluated two medical examples will be given in the first example we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure in the second example we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation a program in r and s plus that can carry out the analyses described here has been developed and is freely available on the internet

a copula based mixed poisson model for bivariate recurrent events under event dependent censoring in many chronic disease processes subjects are at risk of two or more types of events we describe a bivariate mixed poisson model in which a copula function is used to model the association between two gamma distributed random effects the resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process methods for parameter estimation are described for parametric and semiparametric models based on an em algorithm we also consider the issue of event dependent censoring based on one type of event which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study the asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed as well as associated treatment effects because the joint model is fit based on a likelihood consistent estimates are obtained simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach

estimation of excess risk from case control data using aalen s linear regression model we introduce methods for statistical inference in aalen s non parametric linear regression model of disease incidence aalen 1989 statistics in medicine 8 907 925 from nested case control data these methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history the methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case control samples from the colorado plateau uranium miners cohort language en

inclusion intervals of singular values and applications abstract in this paper we improve the brauer type inclusion interval and present a modified brauer type theorem for singular values numerical examples show that our estimation for singular values is more precise than those corresponding results in recent literature moreover we also consider the marginal singular value on the brauer type inclusion interval some applications of our results are presented

qualitative properties of the numerical solution of linear parabolic problems with nonhomogeneous boundary conditions abstract in papers 1 3 we have formulated the conditions of the conservation of the main characteristic properties of the continuous problem to the numerical schemes in the case of homogeneous boundary conditions such properties are the conservation of the nonnegativity and the concavity of the initial function monotonicity in time contractivity and others in this paper we consider similar questions to the problem with nonhomogeneous boundary conditions we analyse the behaviour of the numerical solution in the limit by the time variable on some fixed mesh we also consider the condition of the preservation of the nonnegativity and convexity concavity of the initial function finally we examine the condition of the conservation of the monotonicity in the space variable of the initial function to the numerical solution

inclusion sets for singular values abstract in this paper the following inclusion sets are under certain conditions presented for singular values of a matrix a a ij c n n d a c a 0 i z a i i b b ii and k p a i 1 n j p i a z 0 z a i z a j b b ii b b jj where a i a ii and p i a j a ij 0 or a ji 0 j i for any i 1 2 n b and c a denote the perron root of the nonnegative matrix b b ij satisfying a ij a ji b ij for all i j 1 2 n with i j and the set of all nontrivial circuits in a the associated directed digraph of a respectively subsequently relations between these two results are investigated theoretic analysis and numerical examples show that these estimates are more precise than recent corresponding results in some cases

on an alternative to gerschgorin circles and ovals of cassini an alternative to gerschgorin circles for the localization of the real eigenvalues of a real matrix was studied in 8 in this paper we present a similar alternative to the brauer s theorem on ovals of cassini

on diagonal schur complements of block diagonally dominant matrices it is known that the diagonal schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices j z liu y q huang some properties on schur complements of h matrices and diagonally dominant matrices linear algebra appl 389 2004 365 380 and the same is true for nonsingular h matrices j z liu j c li z t huang x kong some properties of schur complements and diagonal schur complements of diagonally dominant matrices linear algebra appl 428 2008 1009 1030 in this paper we research the properties on diagonal schur complements of block diagonally dominant matrices and prove that the diagonal schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices and the same holds for generalized block strictly diagonally dominant matrices

some integral properties of the heat equation in this paper we consider the one dimensional heat conduction equation on the interval 0 1 we investigate the integrals of the solution u with respect to the space and time variables and the equivalents of the integrals in the numerical solution we give the properties of the functions e e t 10 u x t dx and f 0 1 f x 0 u x t dt we perform the numerical solution applying the so called method 1 we show that with the additional conditions of the nonnegativity preservation and maximum norm contractivity 2 similar statements are valid as in the continuous case

nonparametric estimation of stage occupation probabilities in a multistage model with current status data multistage models are used to describe individuals or experimental units moving through a succession of stages corresponding to distinct states e g healthy diseased diseased with complications dead the resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied traditional survival analysis is the simplest example of a multistage model where individuals begin in an initial stage say alive and move irreversibly to a second stage death in this article we consider general multistage models with a directed tree structure progressive models in which individuals traverse through stages in a possibly non markovian manner we construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards empirical calculations of these quantities are not possible due to the lack of complete data we consider current status information which represents a more severe form of censoring than the commonly used right censoring asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators finite sample behavior of our estimators is studied by simulation in which we show that our estimators based on these limited data compare well with those based on complete data we also apply our method to a real life data set arising from a cardiovascular diseases study in taiwan

singularity wielandt s lemma and singular values in this study some upper and lower bounds for singular values of a general complex matrix are investigated according to singularity and wielandt s lemma of matrices especially some relationships between the singular values of the matrix a and its block norm matrix are established based on these relationships one may obtain the effective estimates for the singular values of large matrices by using the lower dimension norm matrices in addition a small error in piazza 2002 g piazza t politi an upper bound for the condition number of a matrix in spectral norm j comput appl math 143 1 2002 141 144 is also corrected some numerical experiments on saddle point problems show that these results are simple and sharp under suitable conditions

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

further results on the non parametric linear regression model in survival analysis this paper gives further developments of a non parametric linear regression model in survival analysis three subjects are studied first martingale residuals originally developed for the cox model are introduced for our linear model their theory is developed and they are shown to be useful for judging goodness of fit the second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation in particular this is applied to judging whether the effect of a covariate disappears over time a problem for which no formal test exists the third subject is density type or kernel estimation of the regression functions themselves this might give more direct information than the cumulative plots the approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx and by survival times of grafts in renal patients

doubly diagonally dominant matrices we consider the class of doubly diagonally dominant matrices a ajj e c la 1 l jjl ck i laiklck jlajkl i j and its subclasses we give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an h matrix as in the case of diagonal dominance we show that the schur complements of doubly diagonally dominant matrices inherit this property moreover we describe when a schur complement of a strictly doubly diagonally dominant matrix is strictly diagonally dominant 0 elsevier science inc 1997 1 preliminaries

direct modeling of regression effects for transition probabilities in the progressive illness death model in this work we present direct regression analysis for the transition probabilities in the possibly non markov progressive illness death model the method is based on binomial regression where the response is the indicator of the occupancy for the given state along time randomly weighted score equations that are able to remove the bias due to censoring are introduced by solving these equations one can estimate the possibly time varying regression coefficients which have an immediate interpretation as covariate effects on the transition probabilities the performance of the proposed estimator is investigated through simulations we apply the method to data from the registry of systematic lupus erythematosus relesser a multicenter registry created by the spanish society of rheumatology specifically we investigate the effect of age at lupus diagnosis sex and ethnicity on the probability of damage and death along time copyright 2017 john wiley sons ltd

on three classes of matrices with variants of the diagonal dominance property abstract we introduce three new classes jgd n ludd n and dwdd n of n n complex matrices with variants of the diagonal dominance property each of the three classes contains singular matrices we investigate in depth the relations between the three classes and their relations with the classes of diagonally dominant and generalized diagonally dominant matrices we also study the problem of providing necessary and sufficient conditions for the singularity of a matrix in each of the three classes jgd n ludd n and dwdd n we present an application of the theory of the classes jgd n ludd n and dwdd n to the iterative jacobi method for the solution of the linear system a x b

generalizations of the ostrowski brauer theorem abstract the main theorem of this paper which generalizes the ostrowski brauer theorem and its previous extensions provides conditions necessary and sufficient for the singularity of an irreducible matrix a a ij c n n satisfying the conditions a ii a jj r i a r j a where r k a j k a kj k 1 n for all i j such that aij aji 0 and implies a new description of the location of matrix eigenvalues in terms of ovals of cassini and gerschgorin circles

additive hazards markov regression models illustrated with bone marrow transplant data summary when there are covariate effects to be considered multi state survival analysis is dominated either by parametric markov regression models or by semiparametric markov regression models using cox s 1972 proportional hazards models for transition intensities between the states the purpose of this research work is to study alternatives to cox s model in a general finite state markov process setting we shall look at two alternative models aalen s 1989 nonparametric additive hazards model and lin ying s 1994 semiparametric additive hazards model the former allows the effects of covariates to vary freely over time while the latter assumes that the regression coefficients are constant over time with the basic tools of the product integral and the functional delta method we present an estimator of the transition probability matrix and develop the large sample theory for the estimator under each of these two models data on 1459 hla identical sibling transplants for acute leukaemia from the international bone marrow transplant registry serve as illustration

theorems on schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems abstract we firstly consider the block dominant degree for i ii block strictly diagonally dominant matrix and their schur complements showing that the block dominant degree for the schur complement of an i ii block strictly diagonally dominant matrix is greater than that of the original grand block matrix then as application we present some disc theorems and some bounds for the eigenvalues of the schur complement by the elements of the original matrix further by means of matrix partition and the schur complement of block matrix based on the derived disc theorems we give a kind of iteration called the schur based iteration which can solve large scale linear systems though reducing the order by the schur complement and the numerical example illustrates that the iteration can compute out the results faster

global and local refinement techniques yielding nonobtuse tetrahedral partitions preservation of basic qualitative properties for example the maximum principle ofthe solution of partial differential equations by its finite element approximations is an important goal in mathematical modelling and simulation nonobtuse tetrahedral partitions and linear finite elements guarantee the validity of the discrete analogues of the maximum principle for a wide class of parabolic and elliptic problems in order to get more accurate approximation we often need to refine the used partitions globally or locally in this paper we first propose two variants of global refinement techniques which produce nonobtuse face to face tetrahedral partitions second we present a new local refinement technique which generates nonobtuse face to face tetrahedral partitions in a neighbourhood of a given vertex

eigenvalue bounds and inequalities using vector aggregation of matrices abstract for matrices partitioned into block form the operation of block vector aggregation which associates with a given matrix a matrix of smaller size is introduced properties of aggregated matrices are analyzed in particular it is shown that in the hermitian case the eigenvalues of a block vector aggregated matrix interlace those of the original matrix by using vector aggregation new eigenvalue bounds and inequalities for normal and hermitian matrices are derived and put in context with the existing ones in particular inequalities interrelating eigenvalues of a block partitioned hermitian matrix with those of its diagonal blocks are obtained also it is shown that the spectral constants characterizing the block partitioning of a hermitian matrix are bounded below by the corresponding constants related to associated vector aggregated matrices

assessing cumulative incidence functions under the semiparametric additive risk model in analyzing competing risks data a quantity of considerable interest is the cumulative incidence function often the effect of covariates on the cumulative incidence function is modeled via the proportional hazards model for the cause specific hazard function as the proportionality assumption may be too restrictive in practice we consider an alternative more flexible semiparametric additive hazards model of biometrika 1994 81 501 514 for the cause specific hazard this model specifies the effect of covariates on the cause specific hazard to be additive as well as allows the effect of some covariates to be fixed and that of others to be time varying we present an approach for constructing confidence intervals as well as confidence bands for the cause specific cumulative incidence function of subjects with given values of the covariates furthermore we also present an approach for constructing confidence intervals and confidence bands for comparing two cumulative incidence functions given values of the covariates the finite sample property of the proposed estimators is investigated through simulations we conclude our paper with an analysis of the well known malignant melanoma data using our method