invertibility of a linear combination of two matrices and partial orderings abstract in this paper we present some results relating different matrix partial orderings and the invertibility of a linear combination of ep matrices

asymptotic stability at infinity for differentiable vector fields of the plane let x r2 d r2 be a differentiable but not necessarily c1 vector field where 0 and d z r2 z denote by r z the real part of z c if for some 0 and for all p r2 d no eigenvalue of dpx belongs to 0 z c r z 0 then a for all p r2 d there is a unique positive semi trajectory of x starting at p b it is associated to x a well defined number i x of the extended real line called the index of x at infinity such that for some constant vector v r2 the following is satisfied if i x is less than zero respectively greater or equal to zero then the point at infinity of the riemann sphere r2 is a repellor respectively an attractor of the vector field x v

global attractivity in monotone and subhomogeneous almost periodic systems abstract a global attractivity theorem is first proved for a class of skew product semiflows then this result is applied to monotone and subhomogeneous almost periodic reaction diffusion equations ordinary differential systems and delay differential equations for their global dynamics

a method for analysis of c 1 continuity of subdivision surfaces a sufficient condition for c1 continuity of subdivision surfaces was proposed by reif comput aided geom design 12 1995 pp 153 174 and extended to a more general setting in d zorin constr approx accepted for publication in both cases the analysis of c1 continuity is reduced to establishing injectivity and regularity of a characteristic map in all known proofs of c1 continuity explicit representation of the limit surface on an annular region was used to establish regularity and a variety of relatively complex techniques were used to establish injectivity we propose a new approach to this problem we show that for a general class of subdivision schemes regularity can be inferred from the properties of a sufficiently close linear approximation and injectivity can be verified by computing the index of a curve an additional advantage of our approach is that it allows us to prove c1 continuity for all valences of vertices rather than for an arbitrarily large but finite number of valences as an application we use our method to analyze c1 continuity of most stationary subdivision schemes known to us including interpolating butterfly and modified butterfly schemes as well as the kobbelt s interpolating scheme for quadrilateral meshes

some results on partial ordering and reverse order law of elements of c algebras abstract in this paper we establish some results relating star left star right star minus ordering and the reverse order law under certain conditions on moore penrose invertible elements of c algebras

stability criteria with nonlinear eigenvalues for diagonalizable nonlinear systems stability of the linear system especially the diagonalizable system can be verified by computing the signs of the real parts of its eigenvalues in this paper we generalize this result to the diagonalizable nonlinear system in terms of nonlinear eigenvalues according to the main results the unique equilibrium point of the diagonalizable system is globally asymptotically stable if a specific set of nonlinear eigenvalues is not positive at each point in the state space

on the centers of the weight homogeneous polynomial vector fields on the plane we classify all centers of a planar weight homogeneous polynomial vector field of weight degree 1 2 3 and 4

partial orderings preorderings and the polar decomposition of matrices abstract when a unique decomposition of a complex rectangular matrix into two components is given then a partial ordering on the domain of one of the components induces a preordering on the whole set of matrices and partial orderings on the domains of both components induce a partial ordering on the whole set in this not we consider the three main partial orderings lo wner star and rank subtractivity on the respective domains of the two components of matrices subjected to polar decomposition a ben israel t n e greville generalized inverses theory and applications wiley new york 1974 p 255 and investigate the resulting pre and partial orderings

spectrum and trace invariance criterion and its statistical applications abstract necessary and sufficient conditions are established for the set of nonzero eigenvalues of the product b a to be invariant with respect to the choice of a generalized inverse b it turns out that the same conditions constitute a criterion for the invariance of trace b a the algebraic result derived is then applied to investigate some properties of canonical correlations in the context of the general gauss markov model m y x 2 v in particular the results of watson 1967 and puntanen 1987 are generalized and a new characterization of the best linear unbiased estimator of x under the model m is established

infimum of a pair of matrices abstract in this paper answers are provided to the following questions given a matrix e1 of order k m does there exist a matrix e2 of order m k m such that the matrix e e 1 e 2 is square idempotent and of the same rank as e1 further when is the choice of e2 unique given a subspace t virtually disjoint with the row span of e1 when does there exist a matrix g g 1 g 2 such that g is square idempotent of rank equal to rank g1 rank e1 and g1 is congruent to e1 mod t these results are then used to determine if a pair of matrices a and b has an infimum in the minus partial order further the existence of the sharp order infimum is studied

inter and extrapolatory properties of matrix partial orderings in this paper we study some matrix partial orderings with respect to the preserving the relation a b for original a or and b and the linear combinations of a and b the property that between above respectively a and below respectively b one can locate convex affine combinations of original matrices will be called interpolatory extrapolatory respectively besides classical orderings we introduce and discuss in the mentioned aspect the notion of f orderings

asymptotic properties of the balanced repeated replication method for sample quantiles inference including variance estimation can be made from stratified samples by selecting a balanced set of subsamples this balanced subsampling method is generically called the balanced repeated replication method in survey data analysis which includes mccarthy s balanced half samples method and its extensions for more general stratified designs we establish the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of interest is the population quantile the consistency results also hold when balanced subsampling is replaced by random subsampling as a key technical prerequisite we prove a bahadurtype representation for sample quantiles in stratified random sampling

further relationships between certain partial orders of matrices and their squares abstract theorem 3 of baksalary and pukelsheim linear algebra appl 151 1991 135 asserts that if both a and b are hermitian nonnegative definite matrices then the star order a b between them and the star order a 2 b 2 between their squares are equivalent and they imply the commutativity property ab ba in this paper relationships between the three conditions mentioned above are reinvestigated in situations where the assumptions on a and b are completely or partially relaxed some results concerning the star order are obtained as corollaries to corresponding results referring to the left star and right star orders introduced by baksalary and mitra linear algebra appl 149 1991 73

local inversion theorems without assuming continuous differentiability is frpchet differentiable at x and that f x0 e isom r r then there exists a neighborhood w off x0 and a function h w u such that h is differentiable at f x0 and h f xo xo 1 3 f h y y yew 1 4 h f xo cf x 1 1 5 the following theorem is a consequence of the classical local inversion function theorem

on globally diffeomorphic polynomial maps via newton polytopes and circuit numbers in this article we analyze the global diffeomorphism property of polynomial maps f mathbb r n rightarrow mathbb r n by studying the properties of the newton polytopes at infinity corresponding to the sum of squares polynomials vert f vert 2 2 this allows us to identify a class of polynomial maps f for which their global diffeomorphism property on mathbb r n is equivalent to their jacobian determinant det jf vanishing nowhere on mathbb r n in other words we identify a class of polynomial maps for which the real jacobian conjecture which was proven to be false in general still holds

injectivity of real polynomial maps and łojasiewicz exponents at infinity in this paper we give a lower bound for the ojasiewicz exponent at infinity of a special class of polynomial maps mathbb r n to mathbb r s s 1 as a consequence we detect a class of polynomial maps mathbb r n to mathbb r n that are global diffeomorphisms if their jacobian determinant never vanishes

asymptotic stability at infinity for bidimensional hurwitz vector fields abstract let x u r 2 be a differentiable vector field set spc x eigenvalues of d x z z u this x is called hurwitz if spc x z c z 0 suppose that x is hurwitz and u r 2 is the complement of a compact set then by adding to x a constant v one obtains that the infinity is either an attractor or a repellor for x v that means i there exists a unbounded sequence of closed curves pairwise bounding an annulus the boundary of which is transversal to x v and ii there is a neighborhood of infinity with unbounded trajectories free of singularities and periodic trajectories of x v this result is obtained after to proving the existence of x r 2 r 2 a topological embedding such that x equals x in the complement of some compact subset of u

on sets of elements in rickart rings induced by partial orders abstract let a be a rickart ring and let a 1 be the set of all regular elements in a the set of all a a such that a b are characterized where b a 1 is given and is the minus partial order in case when a is a rickart ring such sets are characterized for the diamond the left star the right star the left sharp and the right sharp partial orders some recent results of mosic et al on partial orders in b h the algebra of all bounded linear operators on a hilbert space h are thus generalized

inference from stratified samples properties of the linearization jackknife and balanced repeated replication methods the asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization jackknife and balanced repeated replication brr methods in stratified samples are established the results are obtained as l oa within the context of a sequence of finite populations jil with l strata in ji l and are valid for any stratified multistage design in which the primary sampling units psu s are selected with replacement and in which independent subsamples are taken within those psu s selected more than once in addition some exact analytical results on the bias and stability of these alternative variance estimators in the case of ratio estimation are obtained for small l under a general linear regression model

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

further results on generalized and hypergeneralized projectors abstract the notions of generalized and hypergeneralized projectors introduced by gros and trenkler j gro s j trenkler generalized and hypergeneralized projectors linear algebra appl 264 1997 463 474 are revisited on the one hand the present paper provides several new characterizations of these sets and on the other the properties of generalized and hypergeneralized projectors related to various matrix partial orderings are considered moreover the paper demonstrates the usefulness in studying the properties of generalized and hypergeneralized projectors of the representation of complex matrices given in corollary 6 by hartwig and spindelbock r e hartwig k spindelbock matrices for which a and a commute linear and multilinear algebra 14 1984 241 256

properties of the star supremum for arbitrary hilbert space operators abstract we give a simple necessary and sufficient condition for the existence of star supremum for two arbitrary operators on a hilbert space it is shown that the results of hartwig 1979 15 and janowitz 1983 18 when applied to the ring of bounded operators on a hilbert space require much simpler conditions we also give a complete answer to a question stated by hartwig and drazin 1982 in 16 regarding the extremal values of range and null space of the star infimum

on mappings preserving the sharp and star orders abstract the present paper is devoted to the study of linear maps preserving certain relations such as the sharp partial order and the star partial order in semisimple banach algebras and c algebras

the minus order and range additivity abstract we study the minus order on the algebra of bounded linear operators on a hilbert space by giving a characterization in terms of range additivity we show that the intrinsic nature of the minus order is algebraic applications to generalized inverses of the sum of two operators to systems of operator equations and to optimization problems are also presented

foliations and polynomial diffeomorphisms of mathbb r 3 let y f g h mathbb r 3 to mathbb r 3 be a c 2 map and let spec y denote the set of eigenvalues of the derivative dy p when p varies in mathbb r 3 we begin proving that if for some 0 spec y cap epsilon epsilon emptyset then the foliation mathcal f k with k in f g h made up by the level surfaces k constant consists just of planes as a consequence we prove a bijectivity result related to the three dimensional case of jelonek s jacobian conjecture for polynomial maps of mathbb r n

further properties of the star left star right star and minus partial orderings certain classes of matrices are indicated for which the star left star right star and minus partial orderings or some of them are equivalent characterizations of the left star and right star orderings similar to those devised by hartwig and styan linear algebra appl 82 1986 145 for the star and minus orderings are established along with other auxiliary results which are of independent interest as well some inheritance type properties of matrices are also given the class of ep matrices appears to be essential in several points of our considerations

preservers of the left star and right star partial orders abstract let m n f be the set of all n n matrices over the field f where f r or f c we characterize maps on m n f which are surjective and preserve either the left star or the right star order in both directions but are not necessarily additive

a note on the rank subtractivity ordering abstract some well known matrix partial orderings can be created by supplementing the so called rank subtractivity partial ordering by an appropriate preordering in this note a new partial ordering with the same property is introduced this new ordering is seen to be weaker than the other orderings but still preserving some inheritance properties

maps preserving the diamond partial order the present paper is devoted to the study of the diamond partial order in c algebras we characterize linear maps preserving this partial order

on the uniform observability of discrete time nonlinear systems in constructing an observer for a discrete time nonlinear system the system is commonly required to satisfy a certain kind of uniform observability condition that is the state should always be reconstructible from observation windows of a specific length irrespective of the values of the state and inputs in this technical note it is proved that this uniform requirement is unnecessary in the sense that if the initial state and inputs are on a compact set then the uniform observability is derived from its non uniform counterpart

lowner partial ordering and space preordering of hermitian non negative definite matrices abstract if a matrix a is below a matrix b with respect to the lowner partial ordering within the set of hermitian non negative definite matrices then the columns of a are linear combinations of the columns of b in this note the class of all such combinations providing a complete characterization of the lowner partial ordering is presented in addition new results on partial ordering of squares of hermitian non negative definite matrices are given

a sufficient condition in order that the real jacobian conjecture in r 2 holds let f f g r2 r2 be a polynomial map such that det df x y is different from zero for all x y r2 and f 0 0 0 0 we prove that for the injectivity of f it is sufficient to assume that the higher homogeneous terms of the polynomials ffx ggx and ffy ggy do not have real linear factors in common the proofs are based on qualitative theory of dynamical systems

partial orders based on outer inverses classes of outer inverses are used to create new partial orders and unify the classification of some of the old partial orders these classes are then compared with those obtained by using g inverses inner inverses

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

a polynomial counterexample to the markus yamabe conjecture abstract we give a polynomial counterexample to both the markus yamabe conjecture and the discrete markus yamabe problem for all dimensions 3

inference from stratified samples second order analysis of three methods for nonlinear statistics abstract for stratified samples and nonlinear statistics that can be expressed as functions of estimated totals second order asymptotic expansions of the linearization jackknife and balanced repeated replication variance estimators are obtained based on these comparisons are made in terms of their biases some higher order asymptotic equivalence results are also established the special case of a combined ratio estimator is investigated in detail some results on bias reduction achieved by the jack knife and balanced repeated replication estimators of a nonlinear function of totals are also given

quantile estimation with a complex survey design estimation of the finite population distribution function and related statistics such as the median and interquartile range is considered large sample properties of estimators constructed from stratified cluster samples and properties of large sample confidence intervals are established the results are obtained within the context of a sequence of finite populations generated from a superpopulation

on some characterizations of the star partial ordering for matrices and rank subtractivity abstract the main result is that drazin s star partial ordering a b holds if and only if a b and b a b a where a b is defined by a a a b and aa ba and where a b denotes rank subtractivity here a and b are m n complex matrices and the superscript denotes the moore penrose inverse several other characterizations of a b are given with particular emphasis on what extra condition must be added in order that rank subtractivity becomes the stronger star order a key tool is a new canonical form for rank subtractivity connections with simultaneous singular value decompositions schur complements and idempotent matrices are also mentioned

some orders for operators on hilbert spaces in this paper we present some interesting properties of the diamond left right star and sharp orders for operators on hilbert spaces

on polynomial submersions of degree 4 and the real jacobian conjecture in r 2 abstract we prove the following version of the real jacobian conjecture let f p q r 2 r 2 be a polynomial map with nowhere zero jacobian determinant if the degree of p is less than or equal to 4 then f is injective the approach to prove this result leads to a complete classification up to affine change of coordinates of the polynomial submersions of degree 4 in r 2 whose level sets are not all connected

a jackknife variance estimator for unistage stratified samples with unequal probabilities summary existing jackknife variance estimators used with sample surveys can seriously overestimate the true variance under unistage stratified sampling without replacement with unequal probabilities a novel jackknife variance estimator is proposed which is as numerically simple as existing jackknife variance estimators under certain regularity conditions the proposed variance estimator is consistent under stratified sampling without replacement with unequal probabilities the high entropy regularity condition necessary for consistency is shown to hold for the rao sampford design an empirical study of three unequal probability sampling designs supports our findings

some more properties of core partial order in this paper the core partial order introduced by baksalary and trenkler has been studied further new characterizations of the core partial order have been derived relationship between the core partial order and some known partial orders has been also investigated

matrix partial orders through generalized inverses unified theory the unified theory presented here covers as special cases the star order of drazin the minus order of hartwig and nambooripad the sharp order and other partial orders introduced by the author

the minus partial order and the shorted matrix the minus partial order was defined by hartwig 6 weakening the conditions of the star partial order of drazin 5 several new properties of the minus partial order are established the minus partial order is used to redefine the shorted matrix 15 17 and to define the infimum a b and the supremum a b of a pair a b of matrices of the same order the definition of the shorted matrix given here is similar to the krein anderson trapp definition of the shorted positive operator

rank invariance criterion and its application to the unified theory of least squares abstract necessary and sufficient conditions are established for the product ab c to have its rank invariant with respect to the choice of a generalized inverse b in particular cases these conditions coincide with the results of mitra they are discussed also in the statistical context of the unified theory of least squares introduced by rao

planar quasi homogeneous polynomial differential systems and their integrability abstract in this paper we study the quasi homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree using this algorithm we obtain all quasi homogeneous vector fields of degree 2 and 3 the quasi homogeneous polynomial differential systems are liouvillian integrable in particular we characterize all the quasi homogeneous vector fields of degree 2 and 3 having a polynomial rational or global analytical first integral

global asymptotic stability for differentiable vector fields of r2 a let x r2 r2 be a differentiable map not necessarily c1 and let spec x be the set of complex eigenvalues of the derivative dxp when p varies in r2 if for some e 0 spec x 0 e then x is injective b let x r2 r2 be a differentiable vector field such that x 0 0 and spec x z c r z 0 then for all p r2 there is a unique positive trajectory starting at p moreover the limit set of p is equal to 0

partial orderings of matrices referring to singular values or eigenvalues abstract a new partial ordering in the set of complex matrices is defined which is weaker than the star ordering introduced by drazin in 1978 and stronger than the minus ordering introduced by hartwig in 1980 this ordering refers to singular values of matrices and the interest in it was generated by canonical interpretations of the minus and star orderings given by hartwig and styan in 1986 for hermitian matrices a similar ordering referring to eigenvalues is also considered and its connection with a problem concerning distributions of quadratic forms in normal variables is pointed out

algebraic and topological classification of the homogeneous cubic vector fields in the plane tsutomu date and masao iri in di gave an algebraic classification of systems i p x y i q x y where p and q are homogeneous polynomials of degree 2 for this they used the classification of the binary cubic forms and also the simultaneous classification of a linear binary form and a cubic binary form given by the algebraic invariant theory we begin by doing a similar study for systems p x y q x y where p and q are homogeneous polynomials of degree three i e cubic systems the classification s theorem of such systems is based on the classification of fourth order binary forms gurevich in gu did the classification of fourth order binary forms on the field of complex numbers since we did not find the classification on the real domain we adapt gurevich s proof to obtain it in section 1 we give some definitions and preliminary results while in section 2 we give the theorem of classification of fourth order binary forms on the real domain the method used in the proof caley s method let us obtain canonical forms of the fourth order binary forms and the algebraic characteristics section 3 is devoted to obtaining the algebraic classification of systems p x y j q x y where p and q are homogeneous polynomials of degree 3 given an arbitrary system x p q with p and q homogeneous polynomials of degree 3 we can know the equivalence class at which it belongs through the algebraic characteristics in section 4 we study the phase portraits of systems 1 p x y j q x y where p and q are homogeneous polynomials of degree n and p and q have no common factor such systems have been studied by j argemi in a here we give a shorter new proof of his results by using

balanced repeated replication for stratified multistage survey data under imputation abstract balanced repeated replication brr is a popular method for variance estimation in surveys the standard brr method works by first creating a set of balanced pseudoreplicated datasets from the original dataset for a survey estimator the brr variance estimator is the average of squared deviations r where r is the same as but based on the data in the rth pseudoreplicated dataset only but when there are a large number of imputed missing values nonrespondents treating the imputed values as observed data and applying the standard brr variance estimation formula does not produce valid variance estimators intuitively the variation due to imputation can be captured by the brr method if every pseudoreplicated dataset is imputed in exactly the same way as the original dataset is imputed assuming that the dataset contains flags for nonrespondents but when a random imputation method such as random hot deck imputation random ratio imputation or random regression imputation is u

maps that are roots of power series we introduce a class of polynomial maps that we call polynomial roots of powerseries and show that automorphisms with this property generate the automorphism group in any dimension in particular we determine generically which polynomial maps that preserve the origin are roots of powerseries we study the one dimensional case in greater depth

planar embeddings with a globally attracting fixed point abstract we consider sufficient conditions which guarantee that an embedding from the plane r 2 into itself has a unique fixed point we subsequently study sufficient conditions under which there appears a globally attracting fixed point for such an embedding

asymptotic smoothing and the global attractor of a weakly damped kdv equation on the real line abstract the existence of the global attractor of a weakly damped forced korteweg de vries equation in the phase space l 2 r is proved an optimal asymptotic smoothing effect of the equation is also shown namely that for forces in l 2 r the global attractor in the phase space l 2 r is actually a compact set in h 3 r the energy equation method is used in conjunction with a suitable splitting of the solutions the dispersive regularization properties of the equation in the context of bourgain spaces are extensively exploited

on group inverses and the sharp order abstract in this work the group inverse of a matrix is used to define the order on square matrices of index 1 the order is similar to the order of drazin 2 and the minus order of hartwig 6 10 and nambooripad 17 the order and the order are compared and contrasted many conditions are given which assure the equivalence of the various partial orders studied

a relationship between the star and minus orderings abstract the result of hartwig and styan 1986 stating that matrices a and b are star ordered if and only if they are minus ordered and b a b a 1 3 or b a b a 1 4 is extended by considering generalized inverses of a linear combination b a with any 0

on semi star related matrices abstract in this note we introduce semi star related matrices investigate some of their properties and demonstrate how the usual definition of drazin s 1978 star partial ordering can be relaxed

l statistics in complex survey problems we study linear combinations of order statistics l statistics in survey problems with a stratified multistage sampling design two general types of l statistics are considered smooth l statistics with weights generated by a smooth function and nonsmooth l statistics sample quantiles the trimmed sample mean the decile mean and variance the sample lorenz curve and the sample gini s family parameters are examples of smooth lstatistics or functions of smooth l statistics used in survey problems it is shown that under weak conditions the smooth l statistics are asymptotically normal and their asymptotic variances can be consistently estimated by jackknifing for the sample quantiles their asymptotic normality requires more conditions on the finite population distribution functions consistent estimators for the asymptotic variances of the sample quantiles are derived asymptotic validity of the woodruff s confidence intervals for population quantiles is also proved

a jacobian criterion for the simultaneous injectivity on positive variables of linearly parameterized polynomial maps abstract consider a map g r r r n r p r m such that for k r r and x r n g k x l x f k x where l r n r p is a linear map and f k x i 1 r k i x a i v i i 1 r k i x 1 a i 1 x n a in v i a i z 0 n and v i r m are fixed for i 1 r we prove that the partially evaluated map g k r n r p r m is injective on r 0 n for every k r 0 r if and only if for each k r 0 r and x r 0 n the linear derivative map d g k x r n r p r m of g k at x is injective this result is useful for studying the uniqueness or multiplicity of equilibria in conservative systems of chemical reactions under mass action a map such as f would represent the rates of change of concentrations of all or some judiciously selected species the linear map l would represent the time invariant total concentrations to illustrate this application we prove the uniqueness of equilibria in a common pharmacological model of receptor ligand interaction without a customary assumption on rate constants that lets all equilibria be of a strong type known as detailed balance our result extends a theorem of craciun and feinberg applicable to maps of the kind of f that earlier result is directly applicable to models of chemical reactions that include the outflow of all species

efficient estimation of non linear finite population parameters by using non parametrics summary currently high precision estimation of non linear parameters such as gini indices low income proportions or other measures of inequality is particularly crucial we propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population through a non parametric model assisted approach we construct a unique system of survey weights that can be used to estimate any non linear parameter that is associated with any study variable of the survey using a plug in principle based on a rigorous functional approach and a linearization principle the asymptotic variance of the estimators proposed is derived and variance estimators are shown to be consistent under mild assumptions the theory is fully detailed for penalized b spline estimators together with suggestions for practical implementation and guidelines for choosing the smoothing parameters the validity of the method is demonstrated on data extracted from the french labour force survey point and confidence interval estimation for the gini index and the low income proportion are derived theoretical and empirical results highlight our interest in using a non parametric versus a parametric approach when estimating non linear parameters in the presence of auxiliary information

some properties of matrix partial orderings abstract the matrix partial orderings considered are 1 the star ordering and 2 the minus ordering or rank subtractivity both in the set of m n complex matrices and 3 the lowner ordering in the set of m m matrices the problems discussed are 1 inheriting certain properties under a given ordering 2 preserving an ordering under some matrix multiplications 3 relationships between an ordering among direct or kronecker and hadamard products and the corresponding orderings between the factors involved 4 orderings between generalized inverses of a given matrix and 5 preserving or reversing a given ordering under generalized inversions several generalizations of results known in the literature and a number of new results are derived

asymptotic stabilizability of homogeneous polynomial systems of odd degree we give some tools for the construction of the homogeneous feedback witch stabilizes a generic class of single input two dimensional homogeneous systems

feedback stabilization of homogeneous polynomial systems of odd degree in the plane in this paper we give some tools for the construction of homogeneous feedback which stabilizes homogeneous polynomial systems of odd degree in the plane

characterizations of minus and star orders between the squares of hermitian matrices gros linear algebra appl 326 2001 215 developed characterizations of the minus and star partial orders between the squares of hermitian nonnegative definite matrices referring to the concept of the space preordering in the present paper his results are generalized by deleting the nonnegative definiteness assumption and supplemented by alternative characterizations

the 5 canonical system on 3 folds of general type let x be a projective minimal gorenstein 3 fold of general type with canonical singularities we prove that the 5canonical map is birational onto its image

left star and right star partial orderings abstract two partial orderings in the set of complex matrices are introduced by combining each of the conditions a a a b and aa ba which define the star partial ordering with one of the conditions m a m b and m a m b which define the space preordering several properties of these orderings are examined with main emphasis on comparing the new orderings with the star ordering the minus ordering and other related partial orderings moreover some further characterizations of partial orderings in terms of inclusions of appropriate classes of generalized inverses are derived with the main emphasis on characterizations involving reflexive generalized inverses