towers of recollement and bases for diagram algebras planar diagrams and a little beyond abstract the recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor the method is hence adapted to treat sequences that are not necessarily towers by inclusion such as symplectic blob algebras diagram algebra quotients of the type c hecke algebras by carefully reviewing the diagram algebra construction we find a new set of functors interrelating module categories of ordinary blob algebras diagram algebra quotients of the type b hecke algebras at different values of the algebra parameters we show that these functors generalise to determine the structure of symplectic blob algebras and hence of certain two boundary temperley lieb algebras arising in statistical mechanics we identify the diagram basis with a cellular basis for each symplectic blob algebra and prove that these algebras are quasihereditary over a field for almost all parameter choices and generically semisimple that is we give bases for all cell and standard modules

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

complex representations of finite monoids ii highest weight categories and quivers abstract in this paper we continue our study of complex representations of finite monoids we begin by showing that the complex algebra of a finite regular monoid is a quasi hereditary algebra and we identify the standard and costandard modules we define the concept of a monoid quiver and compute it in terms of the group characters of the standard and costandard modules we use our results to determine the blocks of the complex algebra of the full transformation semigroup we show that there are only two blocks when the degree 3 we also show that when the degree 5 the complex algebra of the full transformation semigroup is not of finite representation type answering negatively a conjecture of ponizovskii

a generalized approach for implementing general boundary conditions in the gdq free vibration analysis of plates abstract a new approach for implementing general boundary conditions in the gdq free vibration analysis of rectangular plates is presented in this paper the proposed approach directly couples the boundary conditions with the governing equations and is referred to as the cbcge approach it can be applied to any combination of simply supported clamped and free boundary conditions the generality and accuracy of the cbcge approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners in particular the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed and a new grid point distribution is suggested

a variable order approach to improve differential quadrature accuracy in dynamic analysis differential quadrature dq is a numerical technique which can produce highly accurate results by using a considerably small number of grid points when it is applied to dynamic equations however dq may exhibit dynamic numerical instability the present paper analyzed the sources of dynamic numerical instability through a simple example and the main finding is that dynamic stability is dominated by the grid points near and on boundaries based on this we propose a variable order approach which is characterized by applying different dq schemes to the grid points near boundaries and grid points far away from boundaries numerical examples of both linear and non linear dynamic equations show that the variable order approach presented in this paper may greatly improve dynamic stability producing convincing results

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

the partition algebra and the potts model transfer matrix spectrum in high dimensions we construct generalizations pmn q of the partition algebra pn q martin p p 1996 j algebra 183 319 facilitating a representation theoretic approach to the n site transfer matrix spectrum of a high dimensional q state potts model with magnetic field and source terms and to corresponding dichromatic polynomials for each q we describe the irreducible representation theory of the sequence of algebras p q pn q pn1 q pn 1 q n 0 1 2 approaching the large n limit for each positive integer q we extend the potts model representation n of pn q to a representation of p1n q we show how these potts representations embed in the representation theory of the partition algebras these results together provide a tool with which to examine the nature of physical correlation functions for large n the irreducible content of the potts representations can be summarized by sq endpn q vq n and sq 1 endpn1 q vq n where sq is the symmetric group and vq is the space of states of a potts spin we show how the partition algebra formalism matches up the correlation functions of the potts model and the corresponding absolute spectrum degeneracies of its transfer matrix

hecke algebraic approach to the reflection equation for spin chains we use the structural similarity of certain coxeter artin systems to the yang baxter and reflection equations to convert representations of these systems into new solutions of the reflection equation we construct certain bethe ansatz states for these solutions using a parametrization suggested by abstract representation theory

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

quantum weyl reciprocity and tilting modules quantum weyl reciprocity relates the representation theory of hecke algebras of type a with that of q schur algebras this paper establishes that weyl reciprocity holds integrally i e over the ring q q 1 of laurent polynomials and that it behaves well under base change a key ingredient in our approach involves the theory of tilting modules for q schur algebras new results obtained in that direction include an explicit determination of the ringel dual algebra of a q schur algebra in all cases in particular in the most interesting situation the ringel dual identifies with a natural quotient algebra of the hecke algebra

from time series to linear system part ii exact modelling abstract in the second part of this paper the problem of finding an exact model for a q dimensional infinite time series is considered first a mathematical vocabulary for discussing exact modelling is developed it is then shown how the results of part i guarantee the existence of a most powerful ar model for an observed time series two algorithms for obtaining such an ar model are subsequently derived one of these algorithms gives a shortest lag input output model the problem of obtaining a minimal state space realization of the observed time series is also considered in order to do that realization theory based on the truncated behaviour is developed as an extensive example the classical situation with impulse response measurements is discussed

a ribbon hopf algebra approach to the irreducible representations of centralizer algebras the brauer birman wenzl and type a iwahori hecke algebras abstract we show how the ribbon hopf algebra structure on the drinfel d jimbo quantum groups of types a b c and d can be used to derive formulas giving explicit realizations of the irreducible representations of the iwahori hecke algebras of type a and the birman wenzl algebras we use this derivation to give explicit realizations of the irreducible representations of the brauer algebras as well the derivation is accomplished by way of a combination of techniques from operator algebras quantum groups and the theory of 3 manifold invariants although our applications are in the cases of the quantum groups of types a b c and d most of the aspects of our approach apply in the general setting of ribbon hopf algebras

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

differential quadrature approach for delamination buckling analysis of composites with shear deformation the differential quadrature method dqm is used to analyze the one dimensional buckling of a laminated composite beam plate having an across the width delamination located at an arbitrary depth and an arbitrary location along its span a beam theory with shear deformation is used in formulating the problem several case studies are conducted to examine the buckling response of laminates hosting such a delamination using dqm the system of equilibrium equations and the boundary conditions are transformed into a system of linear algebraic eigenvalue equations that are solved by a standard eigensolver the influences of several parameters that affect the buckling strength of such laminates are investigated the investigated parameters are the shear deformation factor the length of the delamination and the through the thickness and longitudinal positions of the delamination the results verify the accuracy and efficiency of dqm

vibration analysis of spherical structural elements using the gdq method this paper deals with the dynamical behaviour of hemispherical domes and spherical shell panels the first order shear deformation theory fsdt is used to analyze the above moderately thick structural elements the treatment is conducted within the theory of linear elasticity when the material behaviour is assumed to be homogeneous and isotropic the governing equations of motion written in terms of internal resultants are expressed as functions of five kinematic parameters by using the constitutive and the congruence relationships the boundary conditions considered are clamped c simply supported s and free f edge numerical solutions have been computed by means of the technique known as the generalized differential quadrature gdq method these results which are based upon the fsdt are compared with the ones obtained using commercial programs such as abaqus ansys femap nastran straus pro engineer which also elaborate a three dimensional analysis the effect of different grid point distributions on the convergence the stability and the accuracy of the gdq procedure is investigated the convergence rate of the natural frequencies is shown to be fast and the stability of the numerical methodology is very good the accuracy of the method is sensitive to the number of sampling points used to their distribution and to the boundary conditions

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

representations of stochastic processes the purpose of this paper is to extend the deterministic behavioural theory of j c willems to a stochastic setting this extension consists of characterizations of discrete time gaussian processes with rational spectral density

the decomposition matrices of the brauer algebra over the complex field the brauer algebra was introduced by r brauer in 1937 as a tool in invariant theory the problem of determining the cartan decomposition matrix of the brauer algebra over the complex field has remained open since then here we determine this fundamental invariant

vibrations of completely free shallow shells of rectangular planform abstract although much has been written about the free vibrations of rectangular plates having completely free boundaries very little has appeared for the case when the plates have curvature i e shallow shells a solution of the problem is presented here for shells having arbitrary but constant curvature the ritz method is used with displacement functions assumed in the form of polynomials convergence studies were made to determine the number of terms required for reasonable solution accuracy numerical results were obtained for the frequencies and mode shapes of three types of shells circular cylindrical spherical and hyperbolic paraboidal and these are compared with those of a flat plate

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

numerical study of grid distribution effect on accuracy of dq analysis of beams and plates by error estimation of derivative approximation the accuracy of global methods such as the differential quadrature dq approach is usually sensitive to the grid point distribution this paper is to numerically study the effect of grid point distribution on the accuracy of dq solution for beams and plates it was found that the stretching of grid towards the boundary can improve the accuracy of dq solution especially for coarse meshes the optimal grid point distribution corresponding to optimal stretching parameter depends on the order of derivatives in the boundary condition and the number of grid points used the optimal grid distribution may not be from the roots of orthogonal polynomials this differs somewhat from the conventional analysis this paper also proposes a simple and effective formulation for stretching the grid towards the boundary the error distribution of derivative approximation is also studied and used to analyze the effect of grid point distribution on accuracy of numerical solutions copyright 2001 john wiley sons ltd

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

2 d differential quadrature solution for vibration analysis of functionally graded conical cylindrical shell and annular plate structures this paper focuses on the dynamic behavior of functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the first order shear deformation theory fsdt is used to analyze the above moderately thick structural elements the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal that are graded through the thickness from one surface of the shell to the other two different power law distributions are considered for the ceramic volume fraction the homogeneous isotropic material is inferred as a special case of functionally graded materials fgm the governing equations of motion expressed as functions of five kinematic parameters are discretized by means of the generalized differential quadrature gdq method the discretization of the system leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology for the homogeneous isotropic special case numerical solutions are compared with the ones obtained using commercial programs such as abaqus ansys nastran straus pro mechanica very good agreement is observed furthermore the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good different typologies of non uniform grid point distributions are considered finally for the functionally graded material case numerical results illustrate the influence of the power law exponent and of the power law distribution choice on the mechanical behavior of shell structures

a tower construction for the radical in brauer s centralizer algebras abstract in this paper we study the structure of the brauer centralizer algebras in the case that the multiplication constant x is a rational integer several authors have studied the structure of these algebras for generic values of x in particular hans wenzl showed that the brauer algebras can be obtained from jones basic construction and he used that fact to prove that the brauer algebras are semisimple when x is not a rational integer the tower construction is a method to study towers of semisimple algebras hence it does not apply in our case where the algebras in the tower eventually have radicals our first step in this paper is to modify the tower construction so that it does a simultaneous tower construction of the radicals and the semisimple quotients of a tower of algebras the rest of the paper is devoted to describing these constructions explicitly in the brauer algebra case one surprising corollary of this method is a connection between two seemingly distinct criteria for the simplicity of certain subrings of the brauer algebras it is possible to identify explicitly certain subrings of the brauer algebras which are the matrix rings corresponding to irreducible representations in the semisimple case in previous work these authors gave a combinatorial condition for simplicity of these individual matrix rings when x is a rational integer the tower construction gives a second algebraic condition for simplicity it is difficult to see why these two conditions are equivalent however the methods used in this paper make that clear

the first fundamental theorem of invariant theory for the orthosymplectic supergroup we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

the dieck temperley lieb algebras of type b and c in brauer algebras abstract in this paper we will study the dieck temperley lieb algebras of type b n and c n we compute their ranks and describe a basis for each of them by using some results from corresponding brauer algebras and temperley lieb algebras respectively

higher dimensional algebra and topological quantum field theory the study of topological quantum field theories increasingly relies upon concepts from higher dimensional algebra such as n categories and n vector spaces we review progress towards a definition of n category suited for this purpose and outline a program in which n dimensional topological quantum field theories tqfts are to be described as n category representations first we describe a suspension operation on n categories and hypothesize that the k fold suspension of a weak n category stabilizes for k n 2 we give evidence for this hypothesis and describe its relation to stable homotopy theory we then propose a description of n dimensional unitary extended tqfts as weak n functors from the free stable weak n category with duals on one object to the n category of n hilbert spaces we conclude by describing n categorical generalizations of deformation quantization and the quantum double construction

schur weyl duality for the brauer algebra and the ortho symplectic lie superalgebra we give a proof of a schur weyl duality statement between the brauer algebra and the ortho symplectic lie superalgebra mathfrak osp v