a multivariate version of isotonic regression summary a multivariate generalization of isotonic regression is given enabling the study of statistical inference for ordered vector valued parameters or sets of ordered parameters including multivariate extensions of bartholomew s 22 and 4 2 an iterative algorithm for computing multivariate isotonic regression is proposed and studied

testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown suppose that an order restriction is imposed among several p variate normal mean vectors we are interested in testing the homogeneity of these mean vectors under this restriction this problem is a multivariate extension of bartholomew s biometrika 46 1959 36 48 when the covariance matrices are known this problem has been studied by sasabuchi inutsuka and kulatunga hiroshima math j 22 1992 551 560 sasabuchi kulatunga and saito amer j math management sci 18 1998 131 158 and some others in the present paper we consider the case when the covariance matrices are common but unknown we propose a test statistic study its upper tail probability under the null hypothesis and estimate its critical points

multiparameter quantum matrices over skew fields abstract we prove that multiparameter quantum matrices over a skew field can be reduced by applying elementary row and column operations each of which preserve the quantum relations from this we derive a new axiomatic description of the quantum determinant which coincides with the classical approach to commutative determinants the bruhat normal form of quantum matrices is given in terms of quantum principal minors

a test for a multiple isotonic regression problem summary a new procedure for testing the homogeneity of normal mean vectors versus order restricted alternatives is proposed and its performance discussed

row reducing quantum matrices the quantum determinant and the dieudonne determinant abstract we prove that row reducing a quantum matrix yields another quantum matrix for the same parameter q this means that the elements of the new matrix satisfy the same relations as those of the original quantum matrix ring m q n as a corollary we can prove that the image of the quantum determinant in the abelianization of the total ring of quotients of m q n is equal to the dieudonne determinant of the quantum matrix a similar result is proved for the multiparameter quantum determinant

a class of complex symmetric toeplitz operators on hardy and bergman spaces abstract an operator t b h is complex symmetric if there exists a conjugation c on h so that c t c t in this paper we characterize the complex symmetric toeplitz operator on the hardy and bergman space in particular we show that the toeplitz operator induced by the berezin transform of a complex symmetric operator on hardy space is also complex symmetric with the same conjugation however we see that this is not true for bergman space by providing some examples

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

conditions for bound states in a periodic linear chain and the spectra of a class of toeplitz operators in terms of polylogarithm functions conditions for bound states for a periodic linear chain are given within the framework of an exactly solvable non relativistic quantum mechanical model in three dimensional space these conditions express the strength parameter in terms of the distance between two consecutive centres of the chain and of the range interaction parameter this expression can be formulated in terms of polylogarithm functions and in some particular cases in terms of the riemann zeta function an interesting mathematical result is that these expressions also correspond to the spectra of toeplitz complex symmetric operators the non trivial zeros of the riemann zeta function are interpreted as multiple points at the origin of the spectra of these toeplitz operators

on linear maps preserving complex symmetry abstract an operator t on a complex hilbert space h is said to be complex symmetric if there exists a conjugate linear isometric involution c h h so that c t c t this paper is devoted to describing which linear maps leave the class of complex symmetric operators invariant complete characterizations are obtained for several classes of linear maps including similarity transformations surjective linear isometries multiplication operators and certain completely positive maps

on complex symmetric toeplitz operators abstract in this paper we give a characterization of a complex symmetric toeplitz operator t on the hardy space h 2 moreover if t is a complex symmetric toeplitz operator we provide a necessary and sufficient condition for t to be normal finally we investigate these t with finite symbols

on local spectral properties of complex symmetric operators abstract in this paper we study properties of complex symmetric operators in particular we prove that every complex symmetric operator having property or is decomposable moreover we show that complex symmetric operator t has dunford s property c and it satisfies weyl s theorem if and only if its adjoint does

spectre premier de oq mn k image canonique et separation normale abstract given any commutative field k denote r oq mn k the coordinate ring of quantum n n matrices over k and assume q is a nonzero element in k which is not a root of unity recall that r is generated by n2 variables xi i 1 n 2 subject only to the following relations if x y z t is any 2 2 sub matrix of x x i then a yx q 1xy zx q 1xz tz q 1zt ty q 1yt zy yz b tx xt q q 1 yz denote r the k algebra generated by the same variables xi subject to the same relations except relations b which are replaced by c tx xt so that r is just the algebra of regular functions on some quantum affine space of dimension n2 over k the theory of derivative elimination defines a natural embedding spec r spec r and asserts that the canonical image spec r is a union of strata spec w r in the sense of goodearl letzter in cms conf proc vol 22 1998 39 58 where w describes some subset w of p 1 n 2 the sets spec w r 1 spec w r w w define the goodearl letzter h stratification of spec r in the sense of goodearl letzter trans amer math soc 352 2000 1381 1403 in this paper we give the precise description of the set w and we compute its cardinality using that description and the derivative elimination algorithm we can verify theorems 6 3 1 6 3 2 that h spec r has an h normal separation in the sense of goodearl in lecture notes in pure and appl math 210 2000 205 237 so that spec r has normal separation in the sense of brown goodearl trans amer math soc 348 1996 2465 2502 this property was conjectured by k brown and k goodearl since r is auslander regular and cohen macaulay this implies by goodearl lenagan j pure appl algebra 111 1996 123 142 that r is catenary and satisfies the tauvel s height formula

complex symmetric toeplitz operators on the dirichlet space abstract we study when a toeplitz operator t on the dirichlet space of the unit disk is complex symmetric with respect to a class of conjugations and find surprisingly that the case of complex symmetries of toeplitz operators according to these conjugations is very few we also show that if t is complex symmetric then the curve t t must be nowhere winding furthermore the spectrum and invertibility of complex symmetric toeplitz operators are described

complex symmetric monomial toeplitz operators on the unit ball abstract monomial toeplitz operators t z p z q on the weighted bergman space of the unit ball in c n are natural extension of the weighted shift operators in higher dimensions dim ker t z p z q may occur for non trivial case thus complex symmetric phenomena will appear in this paper we completely characterize when the monomial toeplitz operator t z p z q on the weighted bergman space is j a symmetric where j a f z f a z with the symmetric unitary n n matrix a moreover we also determine all possible forms of a such that t z p z q is j a symmetric as an application we construct the weakly closed unital commutative algebra generated by complex symmetric toeplitz operators

multiparametric quantum deformation of the general linear supergroup in the work l d faddeev and his collaborators and subsequently v g drinfeld m jimbo s l woronowicz a new class of hopf algebras was constructed they can be considered as one parametric deformations of either group ring or the universal enveloping algebra of a simple algebraic group in this paper we define and investigate a multiparametric deformation of the general linear supergroup this is the simplest example of some general constructions described in 5 6

complex symmetric operators and interpolation abstract in this note we study the interpolation properties of complex symmetric operators on hilbert spaces we show that under certain conditions the complex symmetricity property is preserved under quadratic interpolation we apply this result to the study of complex symmetric toeplitz operators on weighted hilbert spaces of analytic functions

on complex symmetric operator matrices abstract an operator t l h is said to be complex symmetric if there exists a conjugation j on h such that t j t j in this paper we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications in particular we consider the operator matrix of the form t a b 0 j a j where j is a conjugation on h we show that if a is complex symmetric then t is decomposable if and only if a is furthermore we provide some conditions so that a weyl s theorem holds for the operator matrix t