a m isometric operators in semi hilbertian spaces abstract in this work the concept of m isometry on a hilbert space are generalized when an additional semi inner product is considered this new concept is described by means of oblique projections

tensor product of n isometries abstract a hilbert space operator a is an m isometry if k 0 m 1 k m k a m k a m k 0 we prove that the tensor product of an m isometry a with an n isometry b is an m n 1 isometry this proves a conjecture of botelho and jamison 5 remark 5 1

dirichlet type spaces on the unit ball and joint 2 isometries abstract we obtain a formula that relates the spherical moments of the multiplication tuple on a dirichlet type space to a complex moment problem in several variables this can be seen as the ball analogue of a formula originally invented by richter in 23 we capitalize on this formula to study dirichlet type spaces on the unit ball and joint 2 isometries

a combined integral equation and finite element method for the evaluation of stress intensity factors abstract a combination of the classical finite element and the singular integral equation method with the help of schwarz s alternating method s a m is presented in this way the flexibility of finite element method is complemented by the undisputed power of the singular integral equation method in describing singular fields the result is the creation of a powerful hybrid method convenient for the efficient solution of problems of stress fields containing any type of singularity the examples considered in the paper indicate the excellent approximation obtained by the method even when using only a few classical elements

a representation theorem for cyclic analytic two isometries a bounded linear operator t on a complex separable hilbert space z is called a 2 isometry if t 2t2 2t t i o we say that t is analytic if nn 0 tnt 0 in this paper we show that every cyclic analytic 2 isometry can be represented as multiplication by z on a dirichlet type space d 8 here ze denotes a finite positive borel measure on the unit circle for two measures u and v the 2 isometries obtained as multiplication by z on d 8 and d v are unitarily equivalent if and only if u v we also investigate similarity and quasisimilarity of these 2 isometries and we apply our results to the invariant subspaces of the dirichlet shift

decomposing algebraic m isometric tuples abstract we show that any m isometric tuple of commuting algebraic operators on a hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple our approach applies as well to tuples of algebraic operators that are hereditary roots of polynomials in several variables

a recurrence formula for the direct solution of singular integral equations abstract an iterative method for the solution of singular integral equations is given in this paper by developing a recurrence formula discretizing the above formula by using appropriate quadrature rules the solution of the singular integral equation is given in an extremely simple form the number of numerical operations required for such a solution is considerably reduced when compared to the number of operations required for a classical type of solution illustrative examples are given indicating the efficiency of the method it is shown that the number of operations in this procedure is only half the number of the operations for a typical numerical method the convergence of the method is studied in the space of holder continuous functions in the particular case of plane elasticity more efficient bounds are given in the same case it is proved that the procedure is equivalent to the schwarz s alternating method and convergence is assured 18

the three dimensional euclidean quantum group e 3 q and its r matrix a contraction procedure starting from so 4 q is used to determine the quantum analog e 3 q of the three dimensional euclidean group and the structure of its representations a detailed analysis of the contraction of the r matrix is then performed and its explicit expression has been found the classical limit of r is shown to produce an integrable dynamical system by means of the r matrix the pseudogroup of the noncommutative representative functions is considered it will finally be shown that a further contraction made on e 3 q produces the two dimensional galilei quantum group and this in turn can be used to give a new realization of e 3 q and e 2 1 q

a m isometries on hilbert spaces abstract a bounded linear operator t on a hilbert space h is called an a m isometry for some positive operator a on h and integer m if k 0 m 1 m k m k t k a t k 0 we give some properties of a m isometries in particular we focus on spectral properties and the relation between a m isometries and m isometries also we obtain some dynamic properties of a m isometries as a negative answer to 22 question 1 with an example of an a isometric which is n supercyclic and sufficient conditions for an a m isometry to be not n supercyclic moreover we prove that the perturbation of a m isometry by a bigger class than nilpotent operators is not n supercyclic

surface integral finite element hybrid sifeh method for fracture mechanics an effective surface integral and finite element hybrid sifeh method has been developed to model fracture problems in finite plane domains this hybridization by incrementally linear superposition combines the best features of both component methods finite elements are used to model the finite domain and eventually nonlinearity while continuous distributions of dislocations resulting in surface integral equations are used to model the fracture i e displacement discontinuity this method has been implemented in a computer program and results of representative problems are presented these compare very well with known solutions and they demonstrate the computational advantages of sifeh over other numerical methods including the individual components

singular element construction using a mapping technique conformal mapping regularizes in the new plane the singular stress field around the crack tip so conventional finite elements can be used in the transformed plane the inverse mapping of the above elements gives another class of mapped elements the crack tip mapped element is a singular element thus using various elements the parent elements in the mapped plane we obtain an infinity of singular elements the product elements these singular elements are introduced naturally and have no defect as many other singular elements have

unbounded elements affiliated with c algebras and non compact quantum groups the affiliation relation that allows to include unbounded elements operators into thec algebra framework is introduced investigated and applied to the quantum group theory the quantum deformation of the two fold covering of the group of motions of euclidean plane is constructed a remarkable radius quantization is discovered it is also shown that the quantumsu 1 1 group does not exist on thec algebra level for real value of the deformation parameter

a method of grid optimization for finite element methods a computationally useful criterion for grid optimization is derived based on a measure of the interpolation error associated with the finite element model the result is intended to be used to improve the quality of finite element solutions by changing the location of the nodes within a fixed number of degrees of freedom examples of the application of the criterion are provided the finite element method has become an important tool of engineering analysis and design much of the popularity of the method is due to the freedom that it allows in the construction of the discretized model it has long been realized however that this freedom must be carefully exercised since the quality of the finite element solution greatly depends on how the discretization is performed several methods have been proposed to improve the discretized model in an iterative manner one such method is presented in this paper a natural way of improving the quality of finite element solutions is to increase the number of degrees of freedom the process is normally performed after an initial solution is already available several schemes have been devised to introduce the new degrees of freedom in a selective manner in order to produce the greatest possible improvement of the previous solution this calls for the definition of criteria to identify the regions of the domain where the finite element approximation is poorer the new degrees of freedom are added in these regions by either increasing the order of polynomial approximation inside elements the so called p method or by subdivision of elements or h method the process is continued until a specified accuracy is achieved the quality of the finite element solution may be improved also by optimizing the disposition of the nodes analysts often rely on their experience to construct grids that make an efficient use of the available degrees of freedom it is also possible to improve the quality of existing meshes iteratively using predefined guidelines for the redistribution of the nodes this paper considers the development of such guidelines

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

an isometry plus a nilpotent operator is an m isometry applications abstract we prove that if an isometry a and a nilpotent operator q of order n commute then a q is a strict 2 n 1 isometry as an application of the main result we prove that a q cannot be n supercyclic for any n also we find an m isometry with prescribed spectrum k where k is the closed unit disk or a compact subset of the unit circle

classification of hereditary matrices abstract a classical approach used to obtain basic facts in the theory of square matrices involves an analysis of the relationship between polynomials p in one variable and square matrices t such that p t 0 we consider matrices and operators which satisfy a different type of polynomial constraint let h be a complex hilbert space t be a bounded linear transformation of h t be the adjoint of t and c x y be the algebra of polynomials in x and y with complex coefficients for a polynomial p c x y in two variables with complex coefficients define p t m n 0 p m n t n t m where p m n is the coefficient of ynxm in the expansion of p in a power series about the point 0 0 t is called a root of p if and only if p t 0 note that if p c x y is a polynomial in the single variable x then the definition of p t given here agrees with the classical definition in this paper we study the relationships which p t 0 forces between p and t when t is an algebraic operator i e there exists n 1 and complex numbers a0 an 1 such that 0 a0 a1t an 1tn 1 tn the classification starts with the following observation suppose p c x y and an algebraic operator t l h satisfy p t 0 then certain subspaces of h which are invariant for t must be orthogonal or certain coefficients of p must vanish this leads to the notions of a graph attached to each p c x y and a graph attached to each square matrix t for diagonalizable t a necessary and sufficient graph theoretic condition for solving p t 0 is given for nondiagonalizable t this condition is necessary but not sufficient the use of these graphs does however reduce the problem to the problem of solving the equation p t 0 for t with exactly one or two eigenvalues for t with one eigenvalue we give a necessary and sufficient condition for solving p t 0 this leaves the case of solving p t 0 when t has exactly two eigenvalues this problem mixes algebra involving polynomials with matrix theory we show that it is equivalent to the purely algebraic problem of determining if equations of the form i j eci jxi r j s 0 have solutions of finite support with certain nonvanishing properties we call these equations bi hankel equations subordinate to a given subset e of the lattice of integer pairs i j 0 i m 1 0 j n 1 it turns out that there is an algorithm which uses grobner bases for determining if the type of solution we seek exists and for computing it

algebraic properties of operator roots of polynomials abstract properties of m selfadjoint and m isometric operators have been investigated by several researchers particularly interesting to us are algebraic properties of nilpotent perturbations of such operators mccullough and rodman showed in the nineties that if q n 0 and a is a selfadjoint operator commuting with q then the sum a q is a 2 n 1 selfadjoint operator very recently bermudez martinon and noda proved a similar result for nilpotent perturbations of isometries via a new approach we obtain simple proofs of these results and other generalizations to operator roots of polynomials

some general lagrange interpolations over simplex finite elements with reference to derivative singularities abstract for simplex finite elements the native lagrange family with arbitrarily placed nodes is presented in hierarchy ranking expressions it includes the well known complete lagrange family as well as the mid edge lagrange family to be proposed in this paper this new family enables us to utilize harmonious combinations of interpolations of different orders in finite element analysis as an application of developed simplex interpolations to fracture mechanics where some derivative singularities are needed we then describe the semi radial singularity mapping with examinations of peculiar trial function spaces

some results on higher order isometries and symmetries products and sums with a nilpotent operator abstract we study the sum of an m isometry or an m symmetric operator with a nilpotent operator we also study the product of two m isometries or two n symmetries we obtain several theorems generalizing previous work our method is straightforward and thus offers direct and simple insights into why these theorems are true

on tuples of commuting operators in positive semidefinite inner product spaces abstract this paper is concerned with the study of certain properties of operator tuples on a complex hilbert space h when a semi inner product induced by a positive operator a on h is considered in particular we show that r a t a t for every commuting operator tuple t t 1 t d such that each t k admits an a adjoint operator where r a t and a t denote respectively the a joint spectral radius and the a joint numerical radius of t this study allows to establish that r a t a t t a for every a normal commuting tuple of operators t where t a is denoted to be the a joint operator seminorm of t in addition the a joint spectral radius of an a m isometric tuple of commuting operators is studied

the mapped elements for the solution of cracked bodies abstract using a conformal mapping the singular stress field around crack tips is transformed to a regular one with respect to the new variables thus the displacement field is approximated in the mapped plane the inverse mapping gives shape functions which are not polynomials the strain field obtained after a derivation of the displacement field has the appropriate square root singularity the elements constructed by using this procedure are called mapped elements this simple method was applied with excellent results to the solution of a series of problems

multiparametric quantization of the special linear superalgebra it is shown how using the graded faddeev reshetikhin takhtajan frt formalism one can multiparametrize the quantum superalgebra slq n m since the naive serre chevalley relations are not adequate for the presentation of this algebra the quantization is carried out in the cartan weyl basis the final results can be generalized to any finite dimensional superalgebra with a symmetrizable cartan matrix

quadrilateral element with semi radial singularity mapping the singularity mapping elementology based on the constant and semi radial field conditions is presented in an originally quadrilateral finite element with the complete evaluations of singularities in the stress and strain as well as of the strain energy finiteness it is demonstrated that this singularity element family is highly versatile differences and some identities between the semi radial mapping and the so called quarter point mapping are also examined

the numerical methods for oscillating singularities in elliptic boundary value problems the singularities near the crack tips of homogeneous materials are monotone of type r and r log r depending on the boundary conditions along nonsmooth domains however the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type r sin e log r the method of auxiliary mapping mam introduced by babuska and oh was proven to be successful in dealing with r type singularities however the effectiveness of mam is reduced in handling oscillating singularities this paper deals with oscillating singularities as well as the monotone singularities by extending mam through introducing the power auxiliary mapping and the exponential auxiliary mapping

products of m isometries abstract an operator t on a banach space x is called an m p isometry if it satisfies the equality k 0 m m k 1 m k t k x p 0 for all x x in this paper we prove that if t is an n p isometry s is an m p isometry and they commute then ts is an m n 1 p isometry this result applied to elementary operators of length 1 defined on the hilbert schmidt class proves a conjecture in 11

the hidden group structure of quantum groups strong duality rigidity and preferred deformations a notion of well behaved hopf algebra is introduced reflexivity for strong duality between hopf algebras of drinfeld type and their duals algebras of coefficients of compact semi simple groups is proved a hidden classical group structure is clearly indicated for all generic models of quantum groups moyal product like deformations are naturally found for all frt models on coefficients andc functions strong rigidity hbi2 0 under deformations in the category of bialgebras is proved and consequences are deduced

a simple method for constructing the inhomogeneous quantum group iglq n and its universal enveloping algebra uq igl n we propose a simple and concise method to construct the inhomogeneous quantum group iglq n and its universal enveloping algebra uq igl n our technique is based on embedding an n dimensional quantum space in an n 1 dimensional one as the set xn 1 1 this is possible only if one considers the multiparametric quantum space whose parameters are fixed in a specific way the quantum group iglq n is then the subset of glq n 1 which leaves the xn 1 1 subset invariant for the deformed universal enveloping algebra uq igl n we will show that it can also be embedded in uq gl n 1 provided one uses the multiparametric deformation of u gl n 1 with a specific choice of its parameters

a finite element method for stokes equation using discrete singularity expansion the numerical method presented in this paper for stokes equation with corner singularity includes mainly two steps firstly we solve a simple eigenvalue problem which is one dimension less than the original problem to obtain the discrete expansion of the singularity near the corner secondly we combine the approximation of the singularity and standard finite element basis functions to construct special finite element spaces and solve the original problem in the special spaces on a conventional mesh the numerical examples show the effectiveness of this method

some special interpolation formulae for triangular and quadrilateral elements presented herein are methods to generate special interpolation formulae of the following type i c0 continuous interpolation over triangular elements which induces a given type of singularity for the first derivatives at one of the vertices and yet preserves rigid and constant strain motions ii c1 continuous interpolation over triangular elements which induces a given type of singularity for second derivatives at one of the vertices

discrete boundary conditions for elasticity problems with singularities discrete boundary conditions on an artificial boundary are obtained for the elasticity problems with singularities an iteration method is designed to solve the boundary value problem by using the discrete boundary conditions some numerical results are given which demonstrate the effectiveness of the numerical method

inhomogeneous quantum groups related to two dimensional quantum planes we propose a simple and compact method for deriving quantum groups acting on manin s q and h planes using this method we classify all the rigid motions of the two dimensional quantum planes requiring that these inhomogenous transformations preserve differential structure of the quantum plane we obtain two distinct inhomogenous quantum groups for the q plane and one previously unknown inhomogenous quantum group for the h plane iglh h 2

extension of the method of auxiliary mapping for three dimensional elliptic boundary value problems summary in this paper we extend the method of auxiliary mapping mam introduced by babuska and oh to three dimensions so that the extended mam 3 d mam can eectively handle three dimensional elliptic problems containing the singularities caused by the non smooth domains there are three type of singularities caused by non smoothness of domains in r 3 the vertex the edge and the vertex edge combined singularities to deal with the singularities of these types we present three auxiliary mappings and formulas for the transformed bilinear forms and the transformed linear functionals by these auxiliary mappings then we present 3 d mam and constructions of the blending type elemental mappings for elements containing singularities numerical experiments that show the eectiveness of 3 d mam are provided copyright 2001 john wiley sons ltd

duality for multiparametric quantum gl n we show that the hopf algebra uuq dual to the multiparameter matrix quantum group gluq n may be realized a la sudbery 1990 i e tangent vectors at the identity furthermore we give the cartan weyl basis of uuq and show that this is consistent with the duality we show that as a commutation algebra uuq equivalent to uu sl n c x uu z where z is one dimensional and uu z is a central algebra in uuq however as a co algebra uuq cannot be split in this way and depends on all parameters

fundamental theory of the semi radial singularity mapping with applications to fracture mechanics abstract fundamental theory of the semi radial singularity mapping is presented which yields the necessary singularities in the stress and strain with bounded strain energy in particular the quadrilateral semi radial singularity mapping as well as the triangular one with collapse are described explicitly with some verification example in linear fracture mechanics the trial function spaces due to the conventional polynomial interpolations with these peculiar mappings are examined in detail