the quantum heisenberg group h 1 q the structure of the quantum heisenberg group is studied in the two different frameworks of the lie algebra deformations and of the quantum matrix pseudogroups the r matrix connecting the two approaches together with its classical limit r are explicitly calculated by using the contraction technique and the problems connected with the limiting procedure discussed some unusual properties of the quantum enveloping heisenberg algebra are shown

relativistic and newtonian κ space times the deformations of the galilei algebra and their associated noncommutative newtonian space times are investigated this is done by analyzing the possible nonrelativistic limits of an eleven generator pseudo extended poincare algebra p and their implications for the existence of a first order differential calculus the additional one form needed to achieve a consistent calculus on minkowski space is shown to be related to the additional central generator entering in the p hopf algebra in the process deformations of the extended galilei and galilei algebras are introduced which have respectively a cocycle and a bicrossproduct structure

projective representations of k galilei group the projective representations of the k galilei group are found by contracting the relevant representations of the poincare group the projective multiplier is found it is shown that it is not possible to replace the projective representations of by vector representations of some of its extensions

nonperturbative tricritical exponents of trails i exact enumeration on a triangular lattice as the fugacity of intersections in trails intersecting but non overlapping lattice walks is increased the configurations change from swollen ones with the scaling exponents of self avoiding walks to compact ones separating the two regimes is a potentially new tricritical point with no perturbative renormalisation fixed point associated with it supporting evidence for the existence of a tricritical point its likely location and exponents are computed for the first time from exact enumeration of all trails up to length of fifteen lattice constants on the triangular lattice the divergence of the specific heat indicates the location of the tricritical point generalised ratio and pade methods are used to extract the scaling exponents for the number of configurations and their end to end distance

tricriticality and persistency of trails and silhouettes trails and silhouettes polymers with loops are generated using exact enumeration on a face centred cubic lattice by assigning a tunable fugacity factor with each intersection it is observed that as the fugacity for intersections is increased the trail and silhouette configurations change from swollen to compact ones indicating the existence of tricritical points strong divergence of the specific heats for different path lengths is used to locate these tricritical points the dlog pade scheme is used to compute the corresponding tricritical exponents in the limit of large path lengths the tricritical exponents thus obtained show that these tricritical points are distinct from the usual theta point and that trails and silhouettes do not belong to the saw universality class the tricritical exponents further show that trails and silhouettes do not belong to the same universality class persistency arising from fixing the initial step is also investigated and it is found that odd moments of the persistency obey a power law that can be expressed in terms of the critical exponent nu and the path length l

specific heat and crossover exponents at the tricritical collapse of trails from the exact enumeration on a triangular lattice of trail configurations at the tricritical regime as the fugacity for intersections is increased the authors find phi t 0 68 8 for the crossover exponent and hence alpha t 0 5 2 for the specific heat exponent it indicates the collapse transition of trails to differ from that of polymer chains at the theta point in two dimensions

the induced representations of the κ poincare group the induced representations of the poincare group for the massive case and the massless case are described it is shown that it extends many of the features of the classical case

which deformations of the poincare group we analyse the present status of poincare group in considering it as a fundamental object independent of the minkowski space we examine the observables associated with it after having introduced the notion of kinematical observable we derive the class of deformed poincare groups which are compatible with physics

bicrossproduct structure of the quantum weyl group abstract the quantum weyl group formula associated to a complex simple lie algebra g consists of the quantum group uq g with certain quantum simple reflections w i adjoined let kw be the group algebra of the standard covering w of the weyl group of g here k c we show that formula has the structure of a cocycle bicrossproduct formula kw uq g it consists as an algebra of a cocycle semidirect product by a cocycle action of kw on uq g defined with respect to a certain non abelian cocycle it consists as a coalgebra of an extension by a non abelian dual cocycle the dual of formula is also a bicrossproduct and consists as an algebra of an extension of the dual of uq g by the commutative algebra of functions on w via a cocycle

quantum poincare group related to the kappa poincare algebra the classical r matrix implied by the quantum kappa poincare algebra of lukierski nowicki and ruegg is used to generate a poisson structure on the poincare group a quantum deformation of the poincare group on the hopf algebra level is obtained by a trivial quantization

lattice trails i exact results considers the problem of lattice trails introduced by malakis 1975 1976 the author proves the existence of a finite connective constant and establishes a result for the growth of n step trails tn analogous to the best known result for self avoiding walks tn lambda n expt o n for the honeycomb d 2 and lave s lattice d 3 the author establishes a counting theorem from which one can deduce the exact value of the connective constant lambda for the honeycomb lattice lambda 2 2 square root 2 further it follows that the trail problem is in the same universality class as the self avoiding walk problem for those lattices an exact amplitude relation between trails and self avoiding walks and between dumb bells and trails and self avoiding walks is established the non existence of a counting theorem for arbitrary lattices is established an inequality for the triangular lattice connective constant is proved a high density expansion for lambda for the d dimensional hybercubic lattice is also obtained the author argues that contrary to recent suggestions the model is in the same universality class as the self avoiding walk model

finiteness conditions co frobenius hopf algebras and quantum groups abstract some finiteness conditions for infinite dimensional coalgebras particularly right or left semiperfect coalgebras or co frobenius hopf algebras are studied as well examples of co frobenius hopf algebras are constructed via a hopf algebra structure on an ore extension of a group algebra and it is shown that bicrossproducts of co frobenius hopf algebras are themselves co frobenius

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

persistency studies of trails and silhouettes on square and triangular lattices the authors study the persistencies of trails and silhouettes on two dimensional square and triangular lattices these persistencies are induces by fixing the first step of the walk in the positive x direction trails are walks which are not allowed to overlap on themselves but may self intersect whereas silhouettes are just the shadows of trails associated with each self intersection is an attractive interaction energy epsilon mod epsilon mod thus a fugacity factor f i theta theta eitkbt ei theta where i is the number of intersections may be defined this has the advantage of providing a handle on the temperature and such dependence of persistencies on temperature is studied for the first time in this paper they are found to obey a law that may be expressed as a function of the critical exponents x2k 1l theta approximately lpk nu theta f l where l is the chain length nu is the correlation exponent f l approximately loge l or some weak function of l e g lw where w 1 0 p is a parameter and k 0 1 2

persistency properties of models of polymers on simple cubic and face centred cubic lattices the first four odd moments of the persistence lengths of trails and silhouettes are studied on two different 3d lattices the simple cubic lattice and the face centred cubic lattice variations of the averaged persistence lengths with chain lengths l and inverse temperatures theta are systematically examined it is found that the averaged persistence lengths scale with a scaling law of the form xl2k 1 theta approximately lpk nu theta f l where nu is the correlation exponent p is a parameter k 0 1 2 and f l approximately constant in contrast to the results in 2d where f l approximately loge l

regression analysis of data from a cluster sample abstract for the case of different regression relationships in different subgroups of a finite population only part of which are sampled the extended least squares estimator of any weighted average of the distinct coefficients is derived under assumptions relating only to the first two moments of the distribution of the coefficients under these assumptions the estimator is shown to be the best linear unbiased estimator while under further distributional assumptions it is also the bayesian estimator for a quadratic loss function for the case of unknown variances a method for estimating them from the sample is proposed the empirical estimator thus obtained is shown to perform well by a simulation comparison with the optimal estimator and with other proposed empirical estimators

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

lattice trails ii numerical results for pt i see ibid vol 18 p 567 1985 a numerical study of the properties of lattice trails on the honeycomb square triangular and simple cubic lattices is made critical points are estimated for all lattices and upper and lower bounds established extensive series have been obtained and series analysis of both trail generating functions and mean square end to end distance series are not inconsistent with the conclusion that the problem is in the same universality class as the self avoiding walk problem a pseudo star triangle transformation is defined and the analyticity properties of that function coupled with previous exact results clearly supports that conclusion for the triangular lattice as well as providing excellent unbiased critical point estimates the author also shows that the connective constant for d or 2 dimensional hypercubic trails is strictly greater than the corresponding quantity for saws

lie bi algebra structures for centrally extended two dimensional galilei algebra and their lie poisson counterparts all bi algebra structures for centrally extended galilei algebra are classified the corresponding lie poisson structures on centrally extended galilei group are found

tricritical points of trails their euler digraphs and graphs exact results on the sierpinski gasket the collapse transitions of trails their oriented graphs and silhouettes eulerian digraphs and graphs respectively as the fugacity for crossings is increased are investigated by exact decimation on the 2d sierpinski gasket recursion relations between the generating functions for the three basic configurations on consecutive levels are derived for all models the authors find tricritical points which move along a line in a four dimensional parameter space as the fugacity is varied and terminate at a decoupled first or second order multicritical point it suggests these models belong to distinct universality classes which differ from that of self attracting polymer chains which do not undergo a collapse theta transition on this fractal lattice

systems of seemingly unrelated regression equations with time varying coefficients an interplay of kalman filtering scoring em and minque method abstract this paper gives a detailed description of the implementation of ml estimation using scoring and em for the hyperparameters of a particular econometric state space we also show how the em method can be turned into an on line estimation method and how this procedure relates to an adaptive method of variance component estimation based on minque theory a small simulation study for a single equation model indicates how much can be gained in terms of computer time by using a combination of scoring and em

quantization of γ lie bialgebras abstract we introduce the notion of lie bialgebras where is a group these objects give rise to cocommutative co poisson bialgebras for which we construct quantization functors this enlarges the class of co poisson algebras for which a quantization is known our result relies on our earlier work where we showed that twists of lie bialgebras can be quantized we complement this work by studying the behavior of this quantization under compositions of twists

quantum structure of the motion groups of the two dimensional cayley klein geometries a simultaneous and global scheme of quantum deformation is defined for the set of algebras corresponding to the groups of motions of the two dimensional cayley klein geometries their central extensions are also considered under this unified pattern in both cases some fundamental properties characterizing the classical ck geometries as the existence of a set of commuting involutions contractions and dualities relationships remain in the quantum version

benchmarking small area estimators this paper considers benchmarking issues in the context of small area estimation we find optimal estimators within the class of benchmarked linear estimators under linear constraints this extends existing results for external and internal benchmarking and also links the two necessary and sufficient conditions for self benchmarking are found for an augmented model most results of this paper are found using ideas of orthogonal projection copyright 2013 oxford university press

universal amplitudes ratio at the collapse transition of polymers in two dimensions first values of the universal ratio of the mean square radius of gyration and the mean square end to end distance for 2d linear polymers at their collapse transition are calculated by the scanning simulation method two models are considered i self avoiding walks saws with nearest neighbour attractions for which this ratio is found to be 0 179 or 0 003 at the theta point ii self intersecting trails at their tricritical point for which the value 0 166 or 0 002 is obtained this provides yet another indication that these models may belong to different tricritical universality classes the authors have also computed this ratio for trails at the high temperature limit with non interacting intersections and found 0 141 or 0 001 in excellent agreement with earlier estimates of this ratio for saws in their swollen phase

non perturbative tricritical exponents of trails ii exact enumerations on square and simple cubic lattices for pt i see ibid vol 21 p 773 1988 the authors present exact enumerations of trails self intersecting but non overlapping lattice walks tabulated according to their length l number of intersection i and end to end distance for the square lattice up to l 21 i 7 and for the simple cubic lattice up to l 15 i 5 they introduce a fugacity for intersection to explore the transition to a collapsed phase through a novel tricritical point which is unaccessible by the renormalisation group approach the existence of tricritical points in both lattices is manifested by the divergence of the specific heat the values of the tricritical couplings and exponents are extracted by a dlogpade analysis they find for the three dimensional lattice nu t approximately 0 48 and gamma t approximately 0 43 nu t approximately 0 52 and gamma t approximately 1 25 for the square lattice

the quantum isl 2 c group the classical r matrix implied by the quantum kappa poincare algebra of lukierski nowicki and ruegg is used to generate a poisson structure on the isl 2 c group a quantum deformation of the isl 2 c group on the hopf algebra level is obtained by a trivial quantization

extensions of locally compact quantum groups and the bicrossed product construction abstract in the framework of locally compact quantum groups we study cocycle actions we develop the cocycle bicrossed product construction starting from a matched pair of locally compact quantum groups we define exact sequences and establish a one to one correspondence between cocycle bicrossed products and cleft extensions in this way we obtain new examples of locally compact quantum groups

twisted conformal algebra so 4 2 a new twisted deformation uz so 4 2 of the conformal algebra of the 3 1 dimensional minkowskian spacetime is presented this construction is provided by a classical r matrix spanned by ten weyl poincare generators which generalizes non standard quantum deformations previously obtained for so 2 2 and so 3 2 however by introducing a conformal null plane basis it is found that the twist can indeed be supported by an eight dimensional carrier subalgebra by construction the weyl poincare subalgebra remains as a hopf subalgebra after deformation non relativistic limits of uz so 4 2 are shown to be well defined and they give rise to new twisted conformal algebras of galilean and carroll spacetimes furthermore a difference differential massless klein gordon or wave equation with twisted conformal symmetry is constructed through deformed momenta and position operators the deformation parameter is interpreted as the lattice step on a uniform minkowskian spacetime lattice discretized along two basic null plane directions

the statistics of collapsing square lattice trails with a fixed number of vertices of degree 4 a trail on the square lattice with a fixed number k of vertices of degree 4 is called a k trail we model polymer collapse using k trails by incorporating an interaction energy which is proportional to the number of nearest neighbour contact edges of the trail it is known that the number of square lattice n edge closed open k trails can be bounded above and below to o nk by the number of n step self avoiding circuits walks this along with pattern theorems for self interacting self avoiding circuits and walks are used herein to establish upper and lower bounds to o nk for the collapsing free energy of k trails in terms of self avoiding circuits or walks as appropriate we also use pattern theorems to obtain bounds on the limiting nearest neighbour contact density for collapsing k trails finally we investigate k trails with a fixed density of nearest neighbour contacts and show that their limiting entropy per monomer is independent of k

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

bicovariant differential calculus on quantum groups su q n and so q n following woronowicz s proposal the bicovariant differential calculus on the quantum groupssu q n andso q n is constructed a systematic construction of bicovariant bimodules by using the hat r q matrix is presented the relation between the hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules and theq deformed universal enveloping algebras is given imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined as an application the maurer cartan equations and theq analogue of the structure constants are formulated

q deformed poincare algebra theq differential calculus for theq minkowski space is developed the algebra of theq derivatives with theq lorentz generators is found giving theq deformation of the poincare algebra the reality structure of theq poincare algebra is given the reality structure of theq differentials is also found the real laplacian is constructed finally the comultiplication counit and antipode for theq poincare algebra are obtained making it a hopf algebra

heisenberg xxz model and quantum galilei group the 1d heisenberg spin model with an anisotropy of the xxz type is analysed in terms of the symmetry given by the quantum galilei group gamma q 1 for a chain with an infinite number of sites the authors show that the magnon excitations and the s 1 2 n magnon bound states are determined by the algebra in this case the gamma q 1 symmetry provides a description naturally compatible with the bethe ansatz the recurrence relations determined by gamma q 1 permit one to express the energy of the n magnon bound states in a closed form in terms of tchebischeff polynomials

suq h 0 2 and suq h 2 the classical and quantum q deformations of the su 2 algebra by means of classical harmonic oscillators and their canonical quantization we show that the q deformation of the su 2 lie algebra can be realized at a classical level in the sense of poisson brackets denoted by suq inf not 0 2 and that the canonical quantization of the system leads to the quantum q deformation of the su 2 algebra denoted by suq 2 this means that the q deformation and the h cross quantization are in general two different concepts

kappa deformation of poincare superalgebra with classical lorentz subalgebra and its graded bicrossproduct structure the kappa deformed d 4 poincare superalgebra written in hopf superalgebra form is transformed to the basis with classical lorentz subalgebra generators we show that in such a basis the kappa deformed d 4 poincare superalgebra can be written as a graded bicrossproduct we show that the kappa deformed d 4 superalgebra acts covariantly on a kappa deformed chiral superspace

predicting random effects from finite population clustered samples with response error in many situations there is interest in parameters e g mean associated with the response distribution of individual clusters in a finite clustered population we develop predictors of such parameters using a two stage sampling probability model with response error the probability model stems directly from finite population sampling without additional assumptions and thus is design based the predictors are closely related to best linear unbiased predictors blup that arise from common mixed model methods as well as to model based predictors obtained via super population approaches for survey sampling the context assumes clusters of equal size and equal size sampling of units within clusters target parameters may correspond to clusters realized in the sample as well as nonrealized clusters in either case the predictors are linear and unbiased and minimize the expected mean squared error they correspond to the sum of predictors of responses for realized and nonrealized units in the cluster a

induced representations of quantum 1 1 galilei algebras we develop a systematic method to construct induced representations of quantum algebras the procedure makes use of two hopf algebras with a nondegenerate pairing and a pair of dual bases for them we apply the method on three different quantum deformations of the galilei algebra in 1 1 dimensions we obtain several families of induced representations including some results already known

quantum 2 1 kinematical algebras a global approach in this paper we give an approach to quantum deformations of the 2 1 kinematical lie algebras within a scheme that simultaneously describes all groups of motions of classical geometries in n 3 dimensions we cover at once all the kinematical geometries including the quantum versions of inonu wigner contractions which are defined in a natural way and relate q deformations as expected we thus obtain some q deformations previously known for the three dimensional euclidean and 2 1 poincare algebras and also some new q deformations for these and other kinematical algebras such as the 2 1 de sitter galilei and newton hooke algebras

four dimensional quantum affine algebras and space time q symmetries a global model of the q deformation for the quasiorthogonal lie algebras generating the groups of motions of the four dimensional affine cayley klein ck geometries is obtained starting from the three dimensional deformations it is shown how the main algebraic classical properties of the ck systems can be implemented in the quantum case quantum deformed versions either of the space time or space symmetry algebras poincare 3 1 galilei 3 1 4 d euclidean as well as others appear in this context as particular cases for some of these classical algebras several q deformations are directly obtained

existence of four dimensional polymer collapse i kinetic growth trails abstract we present the results of simulations of kinetic growth trails kgt bond avoiding walks in four dimensions we use a mapping from a kinetic growth model to a static model of self interacting trails isat at a particular temperature to argue that this temperature is precisely the collapse temperature of four dimensional interacting trails to do this we show that the kinetic growth trails behave neither like static non interacting trails which should behave as excluded volume dominated four dimensional polymers that is self avoiding walks or collapsed four dimensional polymers but rather show an intermediate behaviour this is the first indication of collapse in any four dimensional lattice polymer model and so may be helpful in deciding which of the competing models of polymers is a good model in lower dimensions we have calculated various exponents of the kgt model and identified them with certain critical exponents of the static isat problem

real space renormalization group approach to the theta point of a linear polymer in 2 and 3 dimensions abstract we present a real space renormalization group rsrg approach to a model of self avoiding walks saw with attractive interactions which is expected to describe the point transition of linear polymers both in two and in three dimensions the results of our approximations are physically sound and qualitatively consistent with other numerical predictions and theoretical conjectures in particular the collapsed phase is correctly described in the present approach

physics for algebraists non commutative and non cocommutative hopf algebras by a bicrossproduct construction abstract the initial part of this paper presents physics for algebraists in the context of quantum mechanics combined with gravity such physical notions as the yang baxter equations position observables momentum space momentum and position quantization etc are described many readers may wish to just read this initial part of the paper the physics leads to the search for self dual algebraic structures and finally to non commutative and non cocommutative hopf algebras by a bicrossproduct construction the entire paper contains numerous examples the non commutative and non cocommutative hopf algebras are obtained as a simultaneous smash product and smash coproduct and denoted h1 h2 among the examples is one obtained by modifying the weyl algebra we also give the context in which the compatibility requirements on the structure maps reduce to the classical yang baxter equations and an example related to drinfel d s double hopf algebra d h

cross product bialgebras part ii abstract this is the central article of a series of three papers on cross product bialgebras we present a universal theory of bialgebra factorizations or cross product bialgebras with cocycles and dual cocycles we also provide an equivalent co modular co cyclic formulation all known examples as for instance bi or smash doublecross and bicross product bialgebras as well as double biproduct bialgebras and bicrossed or cocycle bicross product bialgebras are now united within a single theory furthermore our construction yields various novel types of cross product bialgebras