a rotation group whose subspace arrangement is not from a real reflection group abstract we exhibit a family of real rotation groups whose subspace arrangements are not contained in that of any real reflection group answering a question of martino and singh

geometrically reductive hopf algebras and their invariants abstract by analogy with the mumford definition of geometrically reductive algebraic group we introduce the concept of geometrically reductive hopf algebra over a field then we prove that if h is a geometrically reductive hopf algebra and a is a commutative finitely generated and locally finite h module algebra then the algebra of invariants a h is finitely generated we also prove that in characteristic 0 a hopf algebra h is geometrically reductive if and only if every finite dimensional h module is semisimple and that in positive characteristic every finite dimensional hopf algebra is geometrically reductive finally we prove that in positive characteristic the quantum enveloping hopf algebras u q sl n n 2 are geometrically reductive for any parameter q 1

system reliability and component importance under dependence a copula approach abstractsystem reliability and component importance are of great interest in reliability modeling especially when the components within the system are dependent we characterize the influence of dependence structures on system reliability and component importance in coherent systems with discrete marginal distributions the effects of dependence are captured through copula theory we extend our framework to coherent multi state system applications of the derived results are demonstrated using a gaussian copula which yields simple interpretations simulations and two examples are presented to demonstrate the importance of modeling dependence when estimating system reliability and ranking of component importance proofs algorithms code and data are provided in supplementary materials available online

on finite generation of symbolic rees rings of space monomial curves and existence of negative curves abstract in this paper we shall study finite generation of symbolic rees rings of the defining ideal of the space monomial curves t a t b t c for pairwise coprime integers a b c such that a b c 1 1 1 if such a ring is not finitely generated over a base field then it is a counterexample to the hilbert s fourteenth problem finite generation of such rings is deeply related to existence of negative curves on certain normal projective surfaces we study a sufficient condition definition 3 6 for existence of a negative curve using it we prove that in the case of a b c 2 a b c a negative curve exists using a computer we shall show that there exist examples in which this sufficient condition is not satisfied

the separating variety for the basic representations of the additive group abstract for a group g acting on an affine variety x the separating variety is the closed subvariety of x x encoding which points of x are separated by invariants we concentrate on the indecomposable rational linear representations v n of dimension n 1 of the additive group of a field of characteristic zero and decompose the separating variety into the union of irreducible components we show that if n is odd divisible by four or equal to two the closure of the graph of the action which has dimension n 2 is the only component of the separating variety in the remaining cases there is a second irreducible component of dimension n 1 we conclude that in these cases there are no polynomial separating algebras

computation of invariants for reductive groups abstract we will give an algorithm for computing generators of the invariant ring for a given representation of a linearly reductive group the algorithm basically consists of a single grobner basis computation we will also show a connection between some open conjectures in commutative algebra and finding good degree bounds for generating invariants

castelnuovo mumford regularity by approximation abstract the castelnuovo mumford regularity of a module gives a rough measure of its complexity we bound the regularity of a module given a system of approximating modules whose regularities are known such approximations can arise naturally for modules constructed by inductive combinatorial means we apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

a copula transformation in multivariate mixed discrete continuous models abstract copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions especially if the density function can be represented as the product of the marginal density functions and the copula density function this leads to both an intuitive interpretation of the conditional distribution and convenient estimation procedures however this is no longer the case for copula models with mixed discrete and continuous marginal distributions because the corresponding density function cannot be decomposed so nicely in this paper we introduce a copula transformation method that allows to represent the density function of a distribution with mixed discrete and continuous marginals as the product of the marginal probability mass density functions and the copula density function with the proposed method conditional distributions can be described analytically and the computational complexity in the estimation procedure can be reduced depending on the type of copula used

weitzenbock derivations of free metabelian lie algebras abstract a nonzero locally nilpotent linear derivation of the polynomial algebra k x d k x 1 x d in several variables over a field k of characteristic 0 is called a weitzenbock derivation the classical theorem of weitzenbock states that the algebra of constants k x d which coincides with the algebra of invariants of a single unipotent transformation is finitely generated similarly one may consider the algebra of constants of a locally nilpotent linear derivation of a finitely generated not necessarily commutative or associative algebra which is relatively free in a variety of algebras over k now the algebra of constants is usually not finitely generated except for some trivial cases this holds for the algebra of constants l d l d of the free metabelian lie algebra l d l d with d generators we show that the vector space of the constants l d l d in the commutator ideal l d l d is a finitely generated k x d module for small d we calculate the hilbert series of l d l d and find the generators of the k x d module l d l d this gives also an infinite set of generators of the algebra l d l d

positive solutions to fourth order singular boundary value problems with integral boundary conditions in abstract spaces abstract under various weaker conditions we establish various results on the existence of positive solutions to fourth order singular boundary value problems with integral boundary conditions in abstract spaces the arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator our results improve and extend that obtained in x zhang m feng w ge existence results for nonlinear boundary value problems with integral boundary conditions in banach spaces nonlinear anal 69 2008 3310 3321 y liu multiple positive solutions to fourth order singular boundary value problems in abstract spaces electron j diff eqns 120 2004 1 13 even in the scalar spaces

solvability of some fourth and higher order singular boundary value problems abstract existence results for a variety of singular fourth order boundary value problems of the form yiv f t y y y are given here our nonlinear term f may be singular at t 0 t 1 y 0 and or y 0 for example some singularities of the type y a and y b are included also we discuss and treat the extension of these results to nth order boundary value problems

mapping toric varieties into low dimensional spaces a smooth d dimensional projective variety x can always be embedded into 2d 1 dimensional space in contrast a singular variety may require an arbitrary large ambient space if we relax our requirement and ask only that the map is injective then any d dimensional projective variety can be mapped injectively to 2d 1 dimensional projective space a natural question then arises what is the minimal m such that a projective variety can be mapped injectively to m dimensional projective space in this paper we investigate this question for normal toric varieties with our most complete results being for segre veronese varieties

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

a minimal integrity basis for the elasticity tensor we definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth order elasticity tensor c decomposing c into its so 3 irreducible components we reduce this problem to finding joint invariants of a triplet a b d where a and b are second order harmonic tensors and d is a fourth order harmonic tensor combining theorems of classical invariant theory and formal computations a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time

degree bounds for syzygies of invariants abstract suppose that g is a linearly reductive group good degree bounds for generators of invariant rings were given in proc amer math soc 129 4 2001 955 here we study minimal free resolutions of invariant rings for finite linearly reductive groups g it was recently shown in adv math 156 1 2000 23 electron res announc amer math soc 7 2001 5 adv math 172 2002 151 that rings of invariants are generated in degree at most the group order g in characteristic 0 this degree bound is a classical result by emmy noether see math ann 77 1916 89 given an invariant ring of a finite linearly reductive group g we prove that the ideal of relations of a minimal set of generators is generated in degree at most 2 g

a counterexample to the fourteenth problem of hilbert in dimension four abstract this paper presents a family of new counterexamples to hilbert s fourteenth problem they are realized as subfields of the rational function field of four variables over a field of characteristic zero of transcendence degree three it was previously not known whether any counterexample could be found as a subfield of a rational function field of four variables or whether counterexamples with minimal transcendence degree three could exist

linear counterexamples to the fourteenth problem of hilbert abstract following ideas of a campo neuen indag math n s 5 1994 253 257 we construct linear counterexamples to the fourteenth problem of hilbert from non linear counterexamples d daigle g freudenburg j algebra 221 1999 528 535 g freudenburg transform groups 5 2000 61 71

multiple positive solutions for singular nth order nonlocal boundary value problems in banach spaces in this paper we consider a class of singular nth order nonlocal boundary value problems in banach spaces the existence of multiple positive solutions for the problem is obtained by using the fixed point index theory of strict set contraction operators to demonstrate the applications of our results two examples are also given in the paper

divisors on rational normal scrolls let a be the homogeneous coordinate ring of a rational normal scroll the ring a is equal to the quotient of a polynomial ring s by the ideal generated by the two by two minors of a scroll matrix with two rows and l catalecticant blocks the class group of a is cyclic and is infinite provided l is at least two one generator of the class group is j where j is the ideal of a generated by the entries of the first column of the positive powers of j are well understood if l is at least two then the nth ordinary power the nth symmetric power and the nth symbolic power coincide and therefore all three nth powers are resolved by a generalized eagon northcott complex the inverse of j in the class group of a is k where k is the ideal generated by the entries of the first row of we study the positive powers of k we obtain a minimal generating set and a grobner basis for the preimage in s of the symbolic power k n we describe a filtration of k n in which all of the factors are cohen macaulay s modules resolved by generalized eagon northcott complexes we use this filtration to describe the modules in a finely graded resolution of k n by free s modules we calculate the regularity of the graded s module k n and we show that the symbolic rees ring of k is noetherian

on the finite generation of additive group invariants in positive characteristic abstract roberts freudenburg and daigle and freudenburg have given the smallest counterexamples to hilbert s fourteenth problem as rings of invariants of algebraic groups each is of an action of the additive group on a finite dimensional vector space over a field of characteristic zero and thus each is the kernel of a locally nilpotent derivation in positive characteristic additive group actions correspond to locally finite iterative higher derivations we set up characteristic free analogs of the three examples and show that contrary to characteristic zero in every positive characteristic the invariants are finitely generated

efficient bayesian inference for gaussian copula regression models a gaussian copula regression model gives a tractable way of handling a multivariate regression when some of the marginal distributions are non gaussian our paper presents a general bayesian approach for estimating a gaussian copula model that can handle any combination of discrete and continuous marginals and generalises gaussian graphical models to the gaussian copula framework posterior inference is carried out using a novel and efficient simulation method the methods in the paper are applied to simulated and real data

analysis of multivariate probit models summary this paper provides a practical simulation based bayesian and non bayesian analysis of correlated binary data using the multivariate probit model the posterior distribution is simulated by markov chain monte carlo methods and maximum likelihood estimates are obtained by a monte carlo version of the em algorithm a practical approach for the computation of bayes factors from the simulation output is also developed the methods are applied to a dataset with a bivariate binary response to a four year longitudinal dataset from the six cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the panel survey of income dynamics

multivariate logit copula model with an application to dental data applications of copulas for multivariate continuous data abound but there are only a few that treat multivariate binary data in the present paper we model multivariate binary data based on copulas using mixtures of max infinitely divisible copulas introduced by joe and hu j multivar anal 1996 57 2 240 265 when applying copulas to binary data the marginal distributions also contribute to the dependence measures we propose the use of covariate information in the copula parameters to obtain a direct effect of a covariate on dependence to deal with model uncertainty due to selecting among several candidate models we use a model averaging technique we apply the model to data from the signal tandmobiel dental study and in particular to four binary responses that refer to caries experience in the mandibular and maxillary left and right molars we aim to model kendall s tau associations between them and examine how covariate information affects these associations we found that there are systematically larger associations between the two mandibular and the two maxillary molars using covariates to model these associations more closely we found that the systematic fluoride and age of the children affect the associations note that such relationships could not have been revealed by methods that focus on the marginal models copyright 2008 john wiley sons ltd

on a class of danielewski surfaces in affine 3 space abstract in l makar limanov on groups of automorphisms of a class of surfaces israel j math 69 1990 250 256 and l makar limanov on the group of automorphisms of a surface x n y p z israel j math 121 2001 113 123 l makar limanov computed the automorphism groups of surfaces in c 3 defined by the equations x n z p y 0 where n 1 and p y is a nonzero polynomial similar results have been obtained by a crachiola a crachiola on automorphisms of danielewski surfaces j algebraic geom 15 2006 111 132 for surfaces with equations x n z y 2 x y 0 where n 2 and 0 0 defined over arbitrary base fields here we consider more general surfaces defined by equations x n z q x y 0 where n 2 and q x y is a polynomial with coefficients in an arbitrary base field k we characterize among them the ones which are danielewski surfaces in the sense of a dubouloz danielewski fieseler surfaces transformation groups 10 2 2005 139 162 and we compute their automorphism groups we study closed embeddings of these surfaces in affine 3 space we show that in general their automorphisms do not extend to automorphisms of the ambient space finally we give explicit examples of c actions on a surface in a c 3 which can be extended holomorphically but not algebraically to c actions on a c 3

factorial algebraic group actions and categorical quotients abstract given an action of an affine algebraic group with only trivial characters on a factorial variety we ask for categorical quotients we characterize existence in the category of algebraic varieties moreover allowing constructible sets as quotients we obtain a more general existence result which for example settles the case of a finitely generated algebra of invariants as an application we provide a combinatorial git type construction of categorical quotients for actions of not necessarily reductive groups on e g complete varieties with finitely generated cox ring via lifting to the characteristic space

on finite generation of kernels of locally nilpotent r derivations of r x y z let r be a noetherian domain containing the field of rationals we show that if r is dedekind then the kernel of any locally nilpotent r derivation of r x y z is a finitely generated r algebra conversely we show that if r is neither a field nor a dedekind domain then there exists a locally nilpotent r derivation of r x y z whose kernel is not finitely generated over r

separating invariants for 2 2 matrices abstract a minimal separating set is found for the algebra of matrix invariants of several 2 2 matrices over an infinite field of arbitrary characteristic

triangular derivations of k x1 x2 x3 x4 abstract it is shown that if k is a field of characteristic zero then the kernel of any triangular k derivation of k x 1 x 2 x 3 x 4 is finitely generated as a k algebra this is obtained as a corollary of a more general result concerning triangular r derivations of r x y z for certain rings r

symmetric positive solutions of boundary value problems with integral boundary conditions under conditions weaker than those used by ma we establish various results on the existence and nonexistence of symmetric positive solutions to fourth order boundary value problems with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in a cone our results improve and extend that obtained in h ma symmetric positive solutions for nonlocal boundary value problems of fourth order nonlinear anal 68 2008 645 651 we illustrate our results by one example which cannot be handled using the existing results

the noether bound in invariant theory of finite groups abstract let r be a commutative ring v a finitely generated free r module and g glr v a finite group acting naturally on the graded symmetric algebra a sym v let ag denote the minimal number m such that the ring ag of invariants can be generated by finitely many elements of degree at most m furthermore let h g be a normal subgroup such that the index g h is invertible in r in this paper we prove the inequality a g a h g h for h 1 and g invertible in r we obtain noether s bound ag g which so far had been shown for arbitrary groups only under the assumption that the factorial of the group order g is invertible in r

pair copula constructions for multivariate discrete data multivariate discrete response data can be found in diverse fields including econometrics finance biometrics and psychometrics our contribution through this study is to introduce a new class of models for multivariate discrete data based on pair copula constructions pccs that has two major advantages first by deriving the conditions under which any multivariate discrete distribution can be decomposed as a pcc we show that discrete pccs attain highly flexible dependence structures second the computational burden of evaluating the likelihood for an m dimensional discrete pcc only grows quadratically with m this compares favorably to existing models for which computing the likelihood either requires the evaluation of 2 m terms or slow numerical integration methods we demonstrate the high quality of inference function for margins and maximum likelihood estimates both under a simulated setting and for an application to a longitudinal discrete dataset on headache severity this article has onli

joint regression analysis for discrete longitudinal data we introduce an approximation to the gaussian copula likelihood of song li and yuan 2009 biometrics 65 60 68 used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes our approximation allows estimation of parameters from response vectors of length much larger than three and is asymptotically equivalent to the gaussian copula likelihood we estimate regression parameters from the toenail infection data of de backer et al 1996 british journal of dermatology 134 16 17 which consist of binary response vectors of length seven or less from 294 subjects although maximizing the gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation gee estimators our simulation study illustrates that for finite samples gee estimators can actually be as much as 20 more efficient

separating invariants and local cohomology the study of separating invariants is a recent trend in invariant theory for a finite group acting linearly on a vector space a separating set is a set of invariants whose elements separate the orbits of g in some ways separating sets often exhibit better behavior than generating sets for the ring of invariants we investigate the least possible cardinality of a separating set for a given g action our main result is a lower bound that generalizes the classical result of serre that if the ring of invariants is polynomial then the group action must be generated by pseudoreflections we find these bounds to be sharp in a wide range of examples

constants of weitzenbock derivations and invariants of unipotent transformations acting on relatively free algebras abstract in commutative algebra a weitzenbock derivation is a nonzero triangular linear derivation of the polynomial algebra k x 1 x m in several variables over a field k of characteristic 0 the classical theorem of weitzenbock states that the algebra of constants is finitely generated this algebra coincides with the algebra of invariants of a single unipotent transformation in this paper we study the problem of finite generation of the algebras of constants of triangular linear derivations of finitely generated not necessarily commutative or associative algebras over k assuming that the algebras are free in some sense in most of the cases relatively free algebras in varieties of associative or lie algebras in this case the algebra of constants also coincides with the algebra of invariants of some unipotent transformation the main results are the following 1 we show that the subalgebra of constants of a factor algebra can be lifted to the subalgebra of constants 2 for all varieties of associative algebras which are not nilpotent in lie sense the subalgebras of constants of the relatively free algebras of rank 2 are not finitely generated 3 we describe the generators of the subalgebra of constants for all factor algebras k x y i modulo a gl 2 k invariant ideal i 4 applying known results from commutative algebra we construct classes of automorphisms of the algebra generated by two generic 2 2 matrices we obtain also some partial results on relatively free lie algebras

a sharp bound for the castelnuovo mumford regularity of subspace arrangements abstract we show that the ideal of an arrangement of d linear subspaces of projective space is d regular in the sense of castelnuovo and mumford answering a question of b sturmfels in particular this implies that the ideal of an arrangement of d subspaces is generated in degrees less than or equal to d

joint regression analysis of correlated data using gaussian copulas this article concerns a new joint modeling approach for correlated data analysis utilizing gaussian copulas we present a unified and flexible machinery to integrate separate one dimensional generalized linear models glms into a joint regression analysis of continuous discrete and mixed correlated outcomes this essentially leads to a multivariate analogue of the univariate glm theory and hence an efficiency gain in the estimation of regression coefficients the availability of joint probability models enables us to develop a full maximum likelihood inference numerical illustrations are focused on regression models for discrete correlated data including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes in the simulation studies the proposed copula based joint model is compared to the popular generalized estimating equations which is a moment based estimating equation method to join univariate glms two real world data examples are used in the illustration

integration of perturbed initial value problems through reduction theory we propose a method to integrate an initial value problem formed by the differential equations of a perturbed dynamical system plus the initial condition the approach consists of several steps first of all if the original system does not enjoy a continuous symmetry it is transformed up to a certain order of approximation m into an equivalent but equivariant one after truncation at order m second this new symmetry allows us to define a reduction map which produces in its whole phase space a splitting of the transformed equations specifically the latter system is decoupled into two subsystems also initial value problems one of them defined in the orbit space associated with the reduction and the other linear in its coordinates as a third step the reduced subsystems are analytically resolved or numerically integrated using standard methods finally the solution of the original system is recovered by inverting back the reduction map and thereafter the analytic transformations we apply our procedure to three examples

multiple solutions of two point boundary value problems of ordinary differential equations in banach spaces soit p un cone normal de l espace de banach reel e on note par n la constante normale de p on considere le probleme aux deux points limites x f t x t i x 0 x 1 ou i 0 1 et f une application continue de i p dans p on etudie l existence de solutions positives multiples

fields defined by locally nilpotent derivations and monomials abstract we prove a necessary and sufficient condition for certain fields defined by locally nilpotent derivations and monomials to be algebraically closed in a rational function field this implies that a counterexample to the fourteenth problem of hilbert in dimension four which was recently given by the author is obtained as the kernel of a derivation it was previously unknown only in dimension four whether there exists such a counterexample

invariant rings and quasiaffine quotients we study hilbert s fourteenth problem from a geometric point of view nagata s celebrated counterexample demonstrates that for an arbitrary group action on a variety the ring of invariant functions need not be isomorphic to the ring of functions of an affine variety in this paper we will show that nevertheless it is always isomorphic to the ring of functions on a quasi affine variety

separating invariants of finite groups this thesis studies separating invariants of finite algebraic groups acting on affine varieties through automorphisms we investigate the question what restrictions does the existence of a separating set of small size or a separating algebra with interesting structural properties impose on the group action theorems of serre dufresne kac watanabe and gordeev and dufresne and jeffries on invariant rings and separating algebras of linear representations are extended to this more general situation

hilbert s fourteenth problem and algebraic extensions let k x be the polynomial ring in n variables over a field k for some n n and k x its field of fractions assume that l is a subfield of k x containing k over which k x is algebraic in spite of being an important issue in hilbert s fourteenth problem relations between finite generation of the k subalgebra l k x of k x and the extension degree k x l of k x over l have not been investigated in the present paper we give an example of l with k x l d such that l k x is not finitely generated for each d n with d 3 for n 3

hilbert s fourteenth problem and field modifications abstract let k x k x 1 x n be the rational function field and k l k x an intermediate field hilbert s fourteenth problem asks whether the k algebra l k x 1 x n is finitely generated various counterexamples to this problem were already given but there are still many open cases in this paper we study the problem in terms of the field theoretic properties of l our result implies that for any s k x 1 x n 1 with k s k x 1 x n 1 and tr deg k k s 2 there exists aut k k x such that k s x n is a counterexample to hilbert s fourteenth problem this implies the existence of several interesting new counterexamples such as one with k x l 2

rings of invariants of certainp groups over the fieldfp abstract we use nakajima s j algebra85 1983 253 286 characterization ofp groups with polynomial rings of invariants over the fieldfpto prove that maximal proper subgroups of such groups have rings of invariants that are hypersurfaces we give an explicit construction for the ring of invariants of such a group as a module over the ring of invariants of the total group

vines a new graphical model for dependent random variables a new graphical model called a vine for dependent random variables is introduced vines generalize the markov trees often used in modelling high dimensional distributions they differ from markov trees and bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence

lengths of tors determined by killing powers of ideals in a local ring given a local ring r and n ideals whose sum is primary to the maximal ideal of r one may define a function which takes an n tuple of exponents a1 an to the length of tork r i1 r in these functions are shown to have rational generating functions in certain cases

estimation of copula models with discrete margins via bayesian data augmentation estimation of copula models with discrete margins can be difficult beyond the bivariate case we show how this can be achieved by augmenting the likelihood with continuous latent variables and computing inference using the resulting augmented posterior to evaluate this we propose two efficient markov chain monte carlo sampling schemes one generates the latent variables as a block using a metropolis hastings step with a proposal that is close to its target distribution the other generates them one at a time our method applies to all parametric copulas where the conditional copula functions can be evaluated not just elliptical copulas as in much previous work moreover the copula parameters can be estimated joint with any marginal parameters and bayesian selection ideas can be employed we establish the effectiveness of the estimation method by modeling consumer behavior in online retail using archimedean and gaussian copulas the example shows that elliptical copulas can be poor at modeling depend

computing invariants of algebraic groups in arbitrary characteristic let g be an affine algebraic group acting on an affine variety x we present an algorithm for computing generators of the invariant ring k x g in the case where g is reductive furthermore we address the case where g is connected and unipotent so the invariant ring need not be finitely generated for this case we develop an algorithm which computes k x g in terms of a so called colon operation from this generators of k x g can be obtained in finite time if it is finitely generated under the additional hypothesis that k x is factorial we present an algorithm that finds a quasi affine variety whose coordinate ring is k x g along the way we develop some techniques for dealing with nonfinitely generated algebras in particular we introduce the finite generation ideal

separating invariants and finite reflection groups abstract a separating algebra is roughly speaking a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants in this paper we introduce a geometric notion of separating algebra this allows us to prove that only groups generated by reflections may have polynomial separating algebras and only groups generated by bireflections may have complete intersection separating algebras

positive solution for m point boundary value problems of fourth order in this paper we consider the existence of positive solutions to the fourth order boundary value problem u u u f t u 0 t 1 u 0 i 1m 2aiu i u 1 i 1m 2biu i u 0 i 1m 2aiu i u 1 i 1m 2biu i where r i 0 1 ai bi 0 for i 1 2 m 2 are given constants satisfying some suitable conditions the proofs are based on the fixed point index theorem in cones

constructing modular separating invariants abstract we consider a finite dimensional modular representation v of a cyclic group of prime order p we show that two points in v that are in different orbits can be separated by a homogeneous invariant polynomial that has degree one or p and that involves variables from at most two summands in the dual representation simultaneously we describe an explicit construction for a separating set consisting of polynomials with these properties

invariants and separating morphisms for algebraic group actions the first part of this paper is a refinement of winkelmann s work on invariant rings and quotients of algebraic group actions on affine varieties where we take a more geometric point of view we show that the algebraic quotient x g given by the possibly not finitely generated ring of invariants is almost an algebraic variety and that the quotient morphism pi x rightarrow x g has a number of nice properties one of the main difficulties comes from the fact that the quotient morphism is not necessarily surjective these general results are then refined for actions of the additive group mathbb g a where we can say much more we get a rather explicit description of the so called plinth variety and of the separating variety which measures how much orbits are separated by invariants the most complete results are obtained for representations we also give a complete and detailed analysis of roberts famous example of a an action of mathbb g a on 7 dimensional affine space with a non finitely generated ring of invariants

a condition for finite generation of the kernel of a derivation abstract we consider a homogeneous derivation on a finitely generated graded normal domain over a field and give a sufficient condition for finite generation of its kernel as its consequence we show some sufficient conditions for finite generation of the kernel of a derivation on a polynomial ring in particular we prove that the kernel of a locally nilpotent monomial derivation on a polynomial ring in four variables is finitely generated

existence results for nonlinear boundary value problems with integral boundary conditions in banach spaces abstract this paper investigates the multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator the nonexistence of positive solution is also studied meanwhile an example is worked out to demonstrate the main results

linear equivalence of ideal topologies it is proved that whenever p is a prime ideal in a commutative noetherian ring such that the p adic and thep symbolic topologies are equivalent then the two topologies are equivalent linearly several explicit examples are calculated in particular for all prime ideals corresponding to non torsion points on nonsingular elliptic cubic curves

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

algebraic density property of danilov gizatullin surfaces a danilov gizatullin surface is an affine surface v which is the complement of an ample section s for the ruling of a hirzebruch surface the remarkable theorem of danilov and gizatullin states that the isomorphism class of v depends only on the self intersection number s s in this paper we apply the theorem of danilov gizatullin to prove that the lie algebra generated by the complete algebraic vector fields on v coincides with the set of all algebraic vector fields of v

a counterexample to hilbert s fourteenth problem in dimension 5 abstract the kernel of a certain triangular derivation of the polynomial ring k x 1 x 2 x 3 x 4 x 5 is shown to be non finitely generated over k a field of characteristic zero thus giving a new counterexample to hilbert s fourteenth problem in the lowest dimension to date

meta analysis of diagnostic tests accounting for disease prevalence a new model using trivariate copulas in real life and somewhat contrary to biostatistical textbook knowledge sensitivity and specificity and not only predictive values of diagnostic tests can vary with the underlying prevalence of disease in meta analysis of diagnostic studies accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects in this paper a new model is proposed using trivariate copulas and beta binomial marginal distributions for sensitivity specificity and prevalence as an expansion of the bivariate model two different copulas are used the trivariate gaussian copula and a trivariate vine copula based on the bivariate plackett copula this model has a closed form likelihood so standard software e g sas proc nlmixed can be used the results of a simulation study have shown that the copula models perform at least as good but frequently better than the standard model the methods are illustrated by two examples