vibration analysis of annular like plates abstract the existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure in this paper the vibration analysis of annular like plates is presented based on numerical and experimental approaches using the finite element analysis code nastran the effects of the eccentricity hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses the results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of recessive modes of the plate with a slightly eccentric hole they will however lead to erroneous results for dominant modes in addition the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate like structures experimental modal analysis on a clamped free annular like plate is performed and the results obtained reveal good agreement with those obtained by numerical analysis this study provides guidance on modal analysis vibration measurement and damage detection of plate like structures

the duality in octonions and the triality principle we show that the existence of an a 2 type subalgebra of e 6 which is dual to another one of g 2 type leads to a definition of the product of octonions on an 8 dimensional subspace of e 6 thisproduct is then only expressed in terms of the lie bracket of e 6 the well knowntriality principle becomes an easy consequence of this definition and g 2 acting by the adjoint action isshown to be the algebra of derivations of the octonions the real octonions are obtained from two specific real forms of e 6

on the approximation of largest common subtrees and largest common point sets this paper considers the approximability of the largest common subtree and the largest common subgraph problems which have applications in molecular biology it is shown that approximating the problems within a factor of ne is np complete while a general search algorithm which approximates both problems within a factor of o n log n is presented moreover several variants of the largest common subtree problem are studied

toeplitz operators and solvable c algebras on hermitian symmetric spaces bounded symmetric domains cartan domains and exceptional domains are higher dimensional generalizations of the open unit disc in this note we give a structure theory for the c algebra t generated by all toeplitz operators tf h p fh with continuous symbol function g c s on the shilov boundary 5 of a bounded symmetric domain d of arbitrary rank r here h belongs to the hardy space h s and p l s h s is the szego projection for domains of rank 1 and tube domains of rank 2 the structure of t has been determined in 1 2 in these cases toeplitz operators are closely related to pseudodifferential operators for the open unit disc t is the c algebra generated by the unilateral shift the structure theory for the general case 12 is based on the fact that d can be realized as the open unit ball of a unique jordan triple system z 7 theorem 4 1 denoting the jordan triple product by uv w a tripotent e g z satisfies ee e e tripotents generalize the partial isometries of matrix algebras and determine the boundary structure of d c z cf 7 theorem 6 3 our principal result 12 cf also 3 4 8 is the following

free vibration of non circular cylindrical shells with longitudinal interior partitions abstract an analysis is presented for the free vibration of a simply supported non circular cylindrical shell with longitudinal interior partitions for this purpose the governing equations of vibration of a non circular cylindrical shell including a plate as special case are written in a matrix differential equation by using the transfer matrix in the circumferential direction once the matrix has been determined the entire structure matrix is obtained by the product of the transfer matrix of the shell and the point matrix at the joint of the structure matrix the method is applied to approximately elliptical cylindrical shells with an interior plate and the natural frequencies and the mode shapes of vibration are calculated numerically giving the results

spectrum and analytical indices of the c algebra of wiener hopf operators we study multivariate generalisations of the classical wiener hopf algebra which is the c algebra generated by the wiener hopf operators given by convolutions restricted to convex cones by the work of muhly and renault this c algebra is known to be isomorphic to the reduced c algebra of a certain restricted action groupoid given by the action of euclidean space on a certain compactification using groupoid methods we construct composition series for the wiener hopf c algebra by a detailed study of this compactification we compute the spectrum and express homomorphisms in k theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms namely these symbols maps turn out to be given by an analytical family index of a continuous family of fredholm operators in a subsequent paper we also obtain a topological expression of these indices

the capelli identity the double commutant theorem and multiplicity free actions 0 the capelli identity cal 3 w p 39 is one of the most celebrated and useful formulas of classical invariant theory w d cl z the double commutant theorem w p 91 is likewise a basic result in the general theory of associative algebras both play key roles in weyl s book the classical groups the main purpose of this paper is to demonstrate a close connection between the two in the context of multiplicity free actions ekj of groups on vector spaces the focus of our discussion will be the structure of the differential operators which commute with a multiplicity free action applications include a new derivation of some formulas of shimura shl and rubenthaler and schiffmann rs for b functions associated to hermitian symmetric spaces and a construction of interesting sets of generators for the center of the universal enveloping algebra of gin we also give a detailed discussion of certain aspects of multiplicity free representations here is an overview of the contents of the paper in sect 1 we review the classical capelli identities we observe how their existence is predicted by a double commutant result 1 6 and 1 8 and we show how they can be used to compute b functions we remark that capelli understood that his operators generate the center of the algebra generated by the polarization operators see b1 p 77 also capelli s motivation in introducing his operators was to explain a formula of cayley essentially the computation of a b function capelli s point of view was remarkably modern and structuralist in certain ways more modern even than that of weyl sections 2 through 9 provide a conceptual context for understanding the capelli identities as a feature of multiplicity free actions they contain a general discussion of the structure of g the algebra of polynomial coefficient differential operators which commute with a given group g of linear transformations the results of the discussion are summarized in theorem 9 1 which says in particular that the polynomial coefficient differential operators commuting with a

singular invariant tempered distributions on regular prehomogeneous vector spaces revue des espaces vectoriels prehomogenes distributions temperees invariantes distributions temperees avec un parametre meromorphe puissances complexes des invariants relatifs soit p x un polynome homogene irreductible a coefficients reels sur un espace vectoriel v soit s x v p x 0 se decompose en un nombre fini de g 1 orbites avec g 1 g gl v p g x p x on pose v 1 uv 2 u uv e v s la decomposition en composantes connexes on donne une condition necessaire et suffisante pour qu une distribution temperee g 1 invariante a support dans s puisse s obtenir comme une combinaison lineaire finie de coefficients de laurent negatifs de la distribution p x s vd i

non parabolic prehomogeneous vector spaces and exceptional lie algebras abstract among the classification of irreducible regular and reduced prehomogeneous vector spaces there are only a few one which are not of parabolic type in this paper we investigate this family of prehomogeneous vector and show that they nevertheless all occur inside the exceptional lie algebras and are in some sense close to the parabolic family moreover we give a lie theoretical description of their relative invariants and the corresponding characters

c algebras of multiplication operators on bergman spaces soit un domaine borne dans c soit a 2 l espace de bergman de toutes les fonctions analytiques sur qui sont de carre integrable par rapport a la mesure volumetrique et soit c la c algebre engendree par les operateurs de multiplication par les fonctions coordonnee sur on etudie les proprietes de c

generalized differential quadrature method for the free vibration of truncated conical panels abstract this paper presents an improved generalized differential quadrature gdq method for the investigation of the effects of boundary conditions on the free vibration characteristics of truncated conical panels the truncated conical panel is an important geometrical shape in the fields of aerospace marine and structural engineering however despite this importance few works in free vibration analysis have dealt with this particular geometry in this work the vibration characteristics of clamped and simply supported truncated conical shells are obtained for various circumferential wave numbers further the effects of the vertex and subtended angles on the frequency parameters are also examined in detail due to limited published results in the open literature results for a range of cases are compared with those generated from the commercial finite element solver mcneal schwendler corporation nastran and excellent agreement is observed

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

racines orthogonales et orbites d algebres de lie semi simple graduees abstract we define a particular class of regular prehomogeneous vector spaces of parabolic type in relation with orthogonal roots on a field of characteristic 0 we give the structure and the orbits of simple elements associated to the nonzero nilpotent elements of the prehomogeneous vector spaces in terms of these orthogonal roots

the natural vibration of a conical shell with an annular end plate in this paper natural frequencies and mode shapes for a conical shell with an annular end plate or a round end plate are investigated in detail by combining the vibration theory with the transfer matrix method the governing equations of vibration for this structure are expressed in terms of a matrix differential equation and a novel recurrence formula method that can close in on analytical solution of transfer matrix is presented once the transfer matrix of single component has been determined and the product of each component matrix and the joining matrix can obtain entire structure matrix the frequency equations and mode shape functions are represented in terms of the elements of the structural transfer matrices the 3d finite element numerical simulations have verified the present formulas of natural frequencies and mode shapes the conclusions show that the transfer matrix method can accurately obtain natural vibration characteristics of the conical shell with an annular end plate

super toeplitz operators and non perturbative deformation quantization of supermanifolds the purpose of this paper is to construct non perturbative deformation quantizations of the algebras of smooth functions on poisson supermanifolds for the examplesu1 1 andcm n algebras of super toeplitz operators are defined with respect to certain hilbert spaces of superholomorphic functions generators and relations for these algebras are given the algebras can be thought of as algebras of quantized functions and deformation conditions are proven which demonstrate the recovery of the super poisson structures in a semi classical limit

a classification of 2 simple prehomogeneous vector spaces of type i let p g gl v be a rational representation of a connected linear algebraic group g on a finite dimensional vector space v all defined over an algebraically closed field k of characteristic zero if v has a zariskidense g orbit we call a triplet g p v a prehomogeneous oector space abbrev p v when p is irreducible such p v s have been classified in 11 since then it has turned out gradually that the complete classification of reductive p v s i e p v s with reductive groups g is an extremely laborious task therefore it is natural to classify some restricted class of p v s e g 2 to get some insight into the general situation a p v g p v is called a 2 simple p v when 1 g gl 1 x g x g with simple algebraic groups g and gz 2 p is the composition of a rational representation p of g x g of the form p p1 0 p pkol a a l l z t with k s t l where pi tv resp pi t are nontrivial irreducible representations of g resp g and the scalar multiplications gz 1 on each irreducible component v for i 1 f where v i v we say that a 2 simple p v g p v is of type zif k l and at least one of gl l xg xg pi pi i 1 k is a nontrivial p v see definition 5 p 43 in 11 on the other hand if k l and all gl l xg xg p op i l k are trivial p v s it is called a 2 simple p v of type ii in 3 all 2 simple p v s of type ii has been already classified in this paper we shall classify all 2simple p v s of type i thus together with 3 we complete a classification of all 2 simple p v s for example the fact that all irreducible p v s are castling equivalent to 2 simple p v s or to x m x y m x g 2 1 1 i i n 1 with m 2 3 see 1 indicates the importance of 2 simple p v s for simplicity we write g p v or g p instead of g p v

racines orthogonales formes quadratiques et orbites d algebres de lie simples graduees abstract we give a unified orbital decomposition for irreducible regular prehomogeneous vector spaces of parabolic type graded by strongly orthogonal roots of same length with one dimensional corresponding root space on a local or global field of characteristic 0 in terms of a class of quadratic forms related to a root system weyl action and the invariants of the prehomogeneous vector spaces

matrix cartan superdomains super toeplitz operators and quantization we present a general theory of non perturbative quantization of a class of hermitian symmetric supermanifolds the quantization scheme is based on the notion of a super toeplitz operator on a suitable z2 graded hilbert spaces of super holomorphic functions the quantized supermanifold arises as the c algebra generated by all such operators we prove that our quantization framework reproduces the invariant super poisson structure on the classical supermanifold as planck s constant tends to zero

on the approximation of shortest common supersequencesand longest common subsequences the problems of finding shortest common supersequences scs and longest common subsequences lcs are two well known bf np hard problems that have applications in many areas including computational molecular biology data compression robot motion planning and scheduling text editing etc a lot of fruitless effort has been spent in searching for good approximation algorithms for these problems in this paper we show that these problems are inherently hard to approximate in the worst case in particular we prove that i scs does not have a polynomial time linear approximation algorithm unless bf p bf np ii there exists a constant delta 0 such that if scs has a polynomial time approximation algorithm with ratio log delta n where n is the number of input sequences then bf np is contained in bf dtime 2 polylog n iii there exists a constant delta 0 such that if lcs has a polynomial time approximation algorithm with performance ratio n delta then bf p bf np the proofs utilize the recent results of arora et al proc 23rd ieee symposium on foundations of computer science 1992 pp 14 23 on the complexity of approximation problems in the second part of the paper we introduce a new method for analyzing the average case performance of algorithms for sequences based on kolmogorov complexity despite the above nonapproximability results we show that near optimal solutions for both scs and lcs can be found on the average more precisely consider a fixed alphabet sigma and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length n moreover assume that the number of input sequences is polynomial in n then there are simple greedy algorithms which approximate scs and lcs with expected additive errors o n 0 707 and o n frac 1 2 epsilon for any epsilon 0 respectively incidentally our analyses also provide tight upper and lower bounds on the expected lcs and scs lengths for a set of random sequences solving a generalization of another well known open question on the expected lcs length for two random sequences k alexander the rate of convergence of the mean length of the longest common subsequence 1992 manuscript v chvatal and d sankoff j appl probab 12 1975 pp 306 315 d sankoff and j kruskall eds time warps string edits and macromolecules the theory and practice of sequence comparison addison wesley reading ma 1983

quotients of some prehomogeneous vector spaces abstract we give quotients v g spec c v g for some prehomogeneous vector spaces g h v

vibration analysis of rotating twisted and open conical shells abstract based on a non linear strain displacement relationship of a non rotating twisted and open conical shell on thin shell theory a numerical method for free vibration of a rotating twisted and open conical shell is presented by the energy method where the effect of rotation is considered as initial deformation and initial stress resultants which are obtained by the principle of virtual work for steady deformation due to rotation then an energy equilibrium of equation for vibration of a twisted and open conical shell with the initial conditions is also given by the principle of virtual work in the two numerical processes the rayleigh ritz procedure is used and the two in plane and a transverse displacement functions are assumed to be algebraic polynomials in two elements the effects of characteristic parameters with respect to rotation and geometry such as an angular velocity and a radius of rotating disc a setting angle a twist angle curvature and a tapered ratio of cross section on vibration performance of rotating twisted and open conical shells are studied by the present method

minimal graded lie algebras and representations of quadratic algebras abstract let g 0 b 0 be a quadratic lie algebra i e a lie algebra g 0 with a non degenerate symmetric invariant bilinear form b 0 and let v be a finite dimensional representation of g 0 we define on g 0 b 0 v v g 0 v a structure of local lie algebra in the sense of kac 4 where the bracket between g 0 and v resp v is given by the representation resp and where the bracket between v and v depends on b 0 and this implies the existence of two z graded lie algebras g m a x g 0 b 0 v and g m i n g 0 b 0 v whose local part is g 0 b 0 v we investigate these graded lie algebras more specifically in the case where g 0 is reductive roughly speaking the map g 0 b 0 v g m i n g 0 b 0 v is a bijection between triplets and a class of graded lie algebras we show that the existence of associated sl 2 triples is equivalent to the existence of non trivial relative invariants on some orbit and we define the graded lie algebras of polynomial type which give rise to some dual airs

toeplitz algebras and rotational automorphisms associated to polydiscs introduction given a bounded symmetric domain d in cm with d being normalized to be circular and to contain the origin upmeier 22 showed that there is a natural way to associate a c algebra to it this c algebra called the toeplitz c algebra of d and denoted 35 is a solvable c algebra with a composition series jk o k n l of length n where n is the rank of the symmetric domain 22 theorem 3 12 we observe that there is a natural group action on 3 by the compact group g of all biholomorphic automorphisms of d which lie in the connected component of the identity and which fix the origin proposition 1 1 every element 0 in g preserves the solvable series jk o k n l of 3 d we thereby obtain a composition series jk x0 z for the crossed product c algebra 3 xo z in this paper we show by introducing the notion of stratification of composition series see section 2 that the series jk x0 z is exactly the maximal radical series of 3 x0 z section 3 and thus obtain an isomorphism invariant for the latter c algebra when is the polydisc d we determine the k theory of the series jk xo z and their subquotients section 4 techniques from k theory using strong morita equivalence yield a complete classification of the c algebras 3 xo z where d is the n dimensional polydisc up to isomorphism for all 0 in g tn

toeplitz c algebras on bounded symmetric domains in this paper we develop a structure theory for the toeplitz c algebra y for an arbitrary bounded symmetric domain d in c classical or exceptional as the main result it is shown that 5y is a c algebra of type i which is solvable i e admits a finite composition sequence of closed ideals sk in 7 such that the subquotients fk i k are continuous fields of elementary c algebras of compact operators the length of this composition sequence coincides with the rank r of d as a hermitian symmetric space for 0 k r the spectral components sk of ay parametrizing the irreducible representations of y are realized in terms of the boundary components complex analytic faces of d the structure theory for y is based on the fact that the tangent space z c c of d carries a jordan algebraic structure z is a jordan triple system with triple product uv w describing the geometry of d in algebraic terms for example d is the open unit ball with respect to the so called spectral norm on z and the boundary components of d are in 1 1 correspondence with the tripotents e e z partial isometries satisfying ee e 4 e in particular the shilov boundary s of d consists of all tripotents of maximal rank r the jordan theoretic description of d was used in 17 to determine an explicit peter weyl decomposition of the hardy space h2 s cf 15 in terms of the norm functions generalized determinants associated with the jordan triple

free vibration of a conical shell with variable thickness abstract an analysis is presented for the free vibration of a truncated conical shell with variable thickness by use of the transfer matrix approach the applicability of the classical thin shell theory is assumed and the governing equations of vibration of a conical shell are written as a coupled set of first order differential equations by using the transfer matrix of the shell once the matrix has been determined by quadrature of the equations the natural frequencies and the mode shapes of vibration are calculated numerically in terms of the elements of the matrix under any combination of boundary conditions at the edges the method is applied to truncated conical shells with linearly parabolically or exponentially varying thickness and the effects of the semi vertex angle truncated length and varying thickness on the vibration are studied

approximation and parameterized algorithms for common subtrees and edit distance between unordered trees given two rooted labeled unordered trees the common subtree problem is to find a bijective matching between subsets of nodes of the trees of maximum cardinality which preserves labels and ancestry relationship the tree edit distance problem is to determine the least cost sequence of insertions deletions and substitutions that converts a tree into another given tree both problems are known to be hard to approximate within some constant factor in general we tackle these problems from two perspectives giving exact algorithms either for special cases or in terms of some parameters and approximation algorithms and hardness of approximation we present a parameterized algorithm in terms of the number of branching nodes that solves both problems and yields polynomial algorithms for several special classes of trees this is complemented with a tighter apx hardness proof that holds when the trees are of height one and two respectively furthermore we present the first approximation algorithms for both problems in particular for the common subtree problem for t trees we present an algorithm achieving a tlog 2 b o p t 1 ratio where b o p t is the number of branching nodes in the optimal solution we also present constant factor approximation algorithms for both problems in the case of bounded height trees

quotients of standard hilbert modules we initiate a study of hilbert modules over the polynomial algebra that are obtained by completing with respect to an inner product having certain natural properties a standard hilbert module is a finite multiplicity version of one of these standard hilbert modules occupy a position analogous to that of free modules of finite rank in commutative algebra and their quotients by submodules give rise to universal solutions of nonlinear relations essentially all of the basic hilbert modules that have received attention over the years are standard including the hilbert module of the shift the hardy and bergman modules of the unit ball modules associated with more general domains in and those associated with projective algebraic varieties we address the general problem of determining when a quotient of an essentially normal standard hilbert module is essentially normal this problem has been resistant our main result is that it can be linearized in that the nonlinear relations defining the submodule can be reduced appropriately to linear relations through an iteration procedure and we give a concrete description of linearized quotients

the berezin transform and invariant differential operators the berezin calculus is important to quantum mechanics creation annihilation operators and operator theory toeplitz operators we study the basic berezin transform linking the contravariant and covariant symbol for all bounded symmetric domains and express it in terms of invariant differential operators

some p v equivalences and a classification of 2 simple prehomogeneous vector spaces of type a classification of 2 simple prehomogeneous vector spaces is completed by using some p v equivalences together with 3 some part is very different from the previous classification of the irreducible or simple cases 1 2 and some new method is necessary this result shows the difficult point of a classification problem of reductive prehomogeneous vector spaces introduction in m sato and t kimura 1 all irreducible prehomogeneous vector spaces abbreviated irreducible p v s are classified up to castling equivalence and it is proved that any irreducible p v is castling equivalent to a 2 simple p v or to sl m x sl m x gl 2 a1 x a1 x a1 with m 2 3 therefore as a step to a classification of the general case it is natural to classify all nonirreducible 2 simple p v s in this paper we shall classify all 2 simple p v s of type ii and give the complete list of them up to strong equivalence in the sense of definition 4 p 36 in 1 however we need various p v equivalences cf propositions 1 7 1 12 1 34 1 36 1 37 theorem 1 16 and its corollary corollary 1 26 definition 1 31 remark 1 32 to carry out the classification and hence first we shall prove them we also investigate the regularity in some cases since all 2 simple p v s of type i are already classified in 3 this completes the classification of all 2 simple p v s here we say that g p v or simply g p is a 2 simple p v if it is a prehomogeneous vector space of the following form g gl 1 k s t xg x g2 where g1 and g2 are simple algebraic groups p the composition of the scalar multiplications gl l k s on each irreducible component and the representation p p1 p 1 pk p k a1 s 1 1 t1 t ofthegroupg1 x g2 where pi aj resp p tj are nontrivial irreducible representations of g1 resp g2 we write g p v instead of g p v for simplicity to avoid confusion we write instead of clearly each gl 1 x g1 x g2 pi p i 1 k is an irreducible 2 simple p v if at least one of them is a nontrivial p v see definition 1 1 we call it a 2 simple p v of type i on the other hand if all of them are trivial p v s we call it a 2 simple p v of type ii in this case we have g2 sl n received by the editors march 3 1986 and in revised form july 30 1986 1980 mathematics subject classification 1985 revision primary 11r20 11r29 secondary 11n25 11r18 01988 american mathematical society 0002 9947 88 1 00 25 per page

poisson structures on affine spaces and flag varieties ii the standard poisson structures on the flag varieties g p of a complex reductive algebraic group g are investigated it is shown that the orbits of symplectic leaves in g p under a fixed maximal torus of g are smooth irreducible locally closed subvarieties of g p isomorphic to intersections of dual schubert cells in the full flag variety g b of g and their zariski closures are explicitly computed two different proofs of the former result are presented the first is in the framework of poisson homogeneous spaces and the second one uses an idea of weak splittings of surjective poisson submersions based on the notion of poisson dirac submanifolds for a parabolic subgroup p with abelian unipotent radical in which case g p is a hermitian symmetric space of compact type it is shown that all orbits of the standard levi factor l of p on g p are complete poisson subvarieties which are quotients of l equipped with the standard poisson structure moreover it is proved that the poisson structure on g p vanishes at all special base points for the l orbits on g p constructed by richardson rohrle and steinberg

quantum b functions of prehomogeneous vector spaces of commutative parabolic type we show that there exist natural q analogues of the b functions for the prehomogeneous vector spaces of commutative parabolic type and calculate them explicitly in each case our method of calculating the b functions seems to be new even for the original case q 1

the complexity of comparing multiply labelled trees by extending phylogenetic tree metrics abstract a multilabeled tree or mul tree is a rooted tree in which every leaf is labelled by an element from some set but in which more than one leaf may be labelled by the same element of that set in phylogenetics such trees are used in biogeographical studies to study the evolution of gene families and also within approaches to construct phylogenetic networks a multilabelled tree in which no leaf labels are repeated is called a phylogenetic tree and one in which every label is the same is also known as a tree shape in this paper we consider the complexity of computing metrics on mul trees that are obtained by extending metrics on phylogenetic trees in particular by restricting our attention to tree shapes we show that computing the metric extension on mul trees is np complete for two well known metrics on phylogenetic trees namely the path difference and robinson foulds distances we also show that the extension of the robinson foulds distance is fixed parameter tractable with respect to the distance parameter the path distance complexity result allows us to also answer an open problem concerning the complexity of solving the quadratic assignment problem for two matrices that are a robinson similarity and a robinson dissimilarity which we show to be np complete we conclude by considering the maximum agreement subtree mast distance on phylogenetic trees to mul trees although its extension to mul trees can be computed in polynomial time we show that computing its natural generalization to more than two mul trees is np complete although fixed parameter tractable in the maximum degree when the number of given trees is bounded

representation and index theory for toeplitz operators we study toeplitz operators on the hardy spaces of connected compact abelian groups and of tube type bounded symmetric domains a representation theorem for these operators and for classes of abstract toeplitz elements in c algebras is proved this is used to give a unified treatment to index theory in this setting and a variety of new index theorems are proved that generalize the gohberg krein theorem for toeplitz operators on the hardy space of the unit circle in the plane

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

natural frequencies of transverse vibrations of non uniform circular and annular plates abstract this paper presents a method for the free transverse vibration analysis of thin elastic isotropic uniform and non uniform circular and annular plates the circumferential mode numbers n 0 and n 1 are dealt with in this paper the method is a hybrid of plate theory and finite element analysis the plate is subdivided into one circular and many annular finite elements two new finite elements were developed the first type being a circular plate and the second an annular plate the displacement functions of the finite element model are the classical solution shape functions of plate theory mass and stiffness matrices are determined by precise analytical integration the free vibrations of uniform circular and annular plates are studied by this method as well as non uniform plates the results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors this method combines the advantages of the standard finite element analysis and the high accuracy formulation provided by the use of displacement functions derived from plate theory instead of the usual low order polynomials the present method is remarkable for the fact that it enables us to determine with equal precision both low and high natural frequencies

index theory for toeplitz operators on bounded symmetric domains in this note we give an index theory for toeplitz operators on the hardy space of the shilov boundary of an arbitrary bounded symmetric domain our results generalize earlier work of gohberg krein and venugopalkrishna 12 for domains of rank 1 and of berger coburn koranyi 1 for domains of rank 2 bounded symmetric domains cartan domains classical or exceptional are the natural higher dimensional analogues of the open unit disk each such domain is homogeneous under a semisimple lie group of biholomorphic transformations and has an essentially unique realization as a convex circular domain which is conveniently described in jordan algebraic terms the underlying vector space z c n carries a jordan triple product denoted by uyv w uv w and the bounded symmetric domain d is the open unit ball of z with respect to the spectral norm 7 the basic example is the space z c of rectangular matrices with jordan triple product uv w uv w wv u 2 giving rise to the hyperbolic matrix ball d z g z spectrum z z 1 the symmetric domains of rank 1 are the smooth hilbert balls in c n for domains d of higher rank r the boundary dd forms a nonsmooth stratified space in jordan algebraic terms the structure of dd can be described as follows an element e z satisfying ee e e is called a tripotent for matrices the tripotents are just the partial isometries every tripotent e induces a splitting of z into the peirce spaces z e z g z ee z xz for a 0 1 the set

boundary orbit strata and faces of invariant cones and complex ol shanskiĭ semigroups let d g k be an irreducible hermitian symmetric domain then g is contained in a complexification gc and there exists a closed complex subsemigroup g gc characterised by fact that all holomorphic discrete series representations of g extend holomorphically to the socalled minimal ol shanskiuo semigroup parallel to the classical theory of boundary strata for the symmetric

reinhardt domains boundary geometry and toeplitz c algebras abstract in this paper we have found explicitly how the boundary geometry of a reinhardt domain in c 2 determines the structure of its toeplitz c algebra more precisely our main result is an explicit simple algorithm to describe the structure of the toeplitz c algebra of a reinhardt domain d in c 2 satisfying some mild boundary condition in terms of rotation c algebras based on the degree of contact of the boundary curve of c the logarithmic domain of d at each point of intersection with the linear faces of the convex hull of c and the slopes of these faces a consequence of this result is that the toeplitz c algebras t d and t d of d and its pseudoconvex hull d are rarely isomorphic but are always of the same type i e either both are of type i or both are not of type i in other words the isomorphism class of t d is usually changed under taking pseudoconvex hull but the type of t d is not affected