noetherian algebras over algebraically closed fields abstract let k be an uncountable algebraically closed field and let a be a countably generated left noetherian k algebra then we show that a k k is left noetherian for any field extension k of k we conclude that all subfields of the quotient division algebra of a countably generated left noetherian domain over k are finitely generated extensions of k we give examples which show that a k k need not remain left noetherian if the hypotheses are weakened

mckay correspondence for symplectic quotient singularities let v be a finite dimensional complex vector space and g sl v a finite subgroup the quotient variety x v g is usually singular if dim v 2 then there exists a canonical smooth projective resolution y x of the singular variety x this resolution is crepant which in this case means that the manifold y has trivial canonical bundle we recall the precise definitions in definition 1 2 the fiber 1 0 y over the singular point 0 x v g is a rational curve whose components are numbered by the nontrivial conjugacy classes in g the homology classes of these components freely generate h2 y q all the other homology groups of y are trivial except for h0 y q q this situation was described by j mckay in mck it is known as the mckay correspondence in higher dimensions the picture splits into two parts one can consider two separate questions 1 when does the quotient x v g admit a smooth crepant resolution y x 2 assuming there exists a smooth crepant resolution y x what can one say about the homology h y q

normality of marsden weinstein reductions for representations of quivers we prove that the marsden weinstein reductions for the moment map associated to representations of a quiver are normal varieties we give an application to conjugacy classes of matrices

blowup subalgebras of the sklyanin algebra we describe some interesting graded rings which are generated by degree 3 elements inside the sklyanin algebra s and prove that they have many good properties geometrically these rings r correspond to blowups of the sklyanin p2 at 7 or fewer points we show that the rings r are exactly those degree 3 generated subrings of s which are maximal orders in the quotient ring of the 3 veronese of s

sklyanin algebras and hilbert schemes of points we construct projective moduli spaces for torsion free sheaves on noncommutative projective planes these moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual commutative projective plane p2 the generic noncommutative plane corresponds to the sklyanin algebra s skl e constructed from an automorphism of infinite order on an elliptic curve e p2 in this case the fine moduli space of line bundles over s with first chern class zero and euler characteristic 1 n provides a symplectic variety that is a deformation of the hilbert scheme of n points on p2 e

idealizer rings and noncommutative projective geometry abstract we study noetherian graded idealizer rings which have very different behavior on the right and left sides in particular we construct noetherian graded algebras t over an algebraically closed field k with the following properties t is left but not right strongly noetherian t kt is left but not right noetherian and t ktop is noetherian the left noncommutative projective scheme t proj is different from the right noncommutative projective scheme proj t and t satisfies left d for some d 2 yet fails right 1

reflection functors and symplectic reflection algebras for wreath products we construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver these functors give equivalences of categories associated to generic parameters which are in the same orbit under the weyl group action we give applications to the representation theory of symplectic reflection algebras of wreath product groups

sheaves on fibered threefolds and quiver sheaves this paper classifies a class of holomorphic d branes closely related to framed torsion free sheaves on threefolds fibered in resolved ade surfaces over a general curve c in terms of representations with relations of a twisted kronheimer nakajima type quiver in the category coh c of coherent sheaves on c for the local calabi yau case c cong bf a 1 and special choice of framing one recovers the n 1 ade quiver studied by cachazo katz vafa

a class of noncommutative projective surfaces let a k a 1 a 2 be a connected graded noetherian k algebra that is generated in degree one over an algebraically closed field k suppose that the graded quotient ring q a has the form q a k y t t 1 sigma where sigma is an automorphism of the integral projective surface y then we prove that a can be written as a naive blowup algebra of a projective surface x birational to y this enables one to obtain a deep understanding of the structure of these algebras for example generically they are not strongly noetherian and their point modules are not parametrized by a projective scheme this is despite the fact that the simple objects in the quotient category qgr a will always be in 1 1 correspondence with the closed points of the scheme x

noncommutative resolutions of ade fibered calabi yau threefolds in this paper we construct noncommutative resolutions of a certain class of calabi yau threefolds studied by cachazo et al geometric transitions and n 1 quiver theories http arxiv org abs hep th 0108120v2 2001 the threefolds under consideration are fibered over a complex plane with the fibers being deformed kleinian singularities the construction is in terms of a noncommutative algebra introduced by ginzburg calabi yau algebras http arxiv org abs math 0612139v2 2006 which we call the n 1 ade quiver algebra

poisson deformations of symplectic quotient singularities abstract we establish a connection between smooth symplectic resolutions and symplectic deformations of a possibly singular affine poisson variety in particular let v be a finite dimensional complex symplectic vector space and g sp v a finite subgroup our main result says that the so called calogero moser deformation of the orbifold v g is in an appropriate sense a versal poisson deformation that enables us to determine the algebra structure on the cohomology h x c of any smooth symplectic resolution x v g multiplicative mckay correspondence we prove further that if g gl h is an irreducible weyl group and v h h then no smooth symplectic resolution of v g exists unless g is of types a b c

finite element prediction of wave motion in structural waveguides a method is presented by which the wavenumbers for a one dimensional waveguide can be predicted from a finite element fe model the method involves postprocessing a conventional but low order fe model the mass and stiffness matrices of which are typically found using a conventional fe package this is in contrast to the most popular previous waveguide fe approach sometimes termed the spectral finite element approach which requires new spectral element matrices to be developed in the approach described here a section of the waveguide is modeled using conventional fe software and the dynamic stiffness matrix formed a periodicity condition is applied the wavenumbers following from the eigensolution of the resulting transfer matrix the method is described estimation of wavenumbers energy and group velocity discussed and numerical examples presented these concern wave propagation in a beam and a simply supported plate strip for which analytical solutions exist and the more complex case of a viscoelastic laminate which involves postprocessing an ansys fe model the method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves

numerical investigation of dispersion relations for helical waveguides using the scaled boundary finite element method abstract in this paper the dispersion properties of elastic waves in helical waveguides are investigated the formulation is based on the scaled boundary finite element method sbefm with a set of orthogonal unit basis introduced as the contravariant basis the helical coordinate is firstly considered where components of tensor retain the dimension of original quantity based on the strain displacement relation the eigenvalue matrix is obtained about wavenumbers and frequencies the cross section of the waveguides is discretized by using high order spectral elements moreover the formulated linear matrix is utilized to design efficient and accurate algorithms to compute the eigenvalues of helical waveguides compared with the pochhammer chree curves the convergence and accuracy of the sbfem are discussed finally we give some dispersion curves for a wide range of lay angles and analyze in detail properties of cut off frequency mode separation and mode transition for elastic wave propagation in the helical waveguides

finite element analysis of the vibrations of waveguides and periodic structures many structural components can be regarded as waveguides they are uniform in one direction so that the cross section of the waveguide has the same physical and geometric properties at all points along the axis of the waveguide in this paper a method is presented to calculate the forced response of such a structure using a combination of wave and finite element fe approaches the method involves post processing a conventional but low order fe model in which the mass and stiffness matrices are typically found using a conventional fe package a section of the waveguide is meshed and the eigenvalues and eigenvectors of the resulting transfer matrix found the eigenvectors form a set of basis functions for the analysis of the structure as a whole allowing the global dynamic stiffness matrix to be built easily and then the forced response to be calculated very efficiently the main advantage of the approach over the alternative waveguide fe approach often termed the spectral fe method is that conventional fe packages can be used to form the stiffness and mass matrices so that structures with complex geometries or material distributions can be analysed with relative ease to demonstrate the efficacy of the method examples of the forced response for a finite beam and plate strip are presented

symplectic resolutions for nilpotent orbits in this paper firstly we calculate picard groups of a nilpotent orbit in a classical complex simple lie algebra and discuss the properties of being factorial and factorial for the normalization tilde of the closure of then we consider the problem of symplectic resolutions for tilde our main theorem says that for any nilpotent orbit in a semi simple complex lie algebra equipped with the kostant kirillov symplectic form if for a resolution z tilde the 2 form defined on 1 extends to a symplectic 2 form on z then z is isomorphic to the cotangent bundle t g p of a projective homogeneous space and is the collapsing of the zero section it proves a conjecture of cho miyaoka shepherd barron in this special case using this theorem we determine all varieties tilde which admit such a resolution

a nonequilibrium entropy for dynamical systems it is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure these are chosen by considering the totality of future possibilities for observation on the system it is shown that this entropy is necessarily a nondecreasing function of the timet there is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal under suitable conditions which are stated explicitly this entropy approaches the equilibrium entropy ast and the fine grained entropy ast in particular the conditions can always be satisfied if the system is ak system as in the sinai billiard models some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition and at the same time elucidate the connection between our concept of entropy and the entropy invariant of kolmogorov and sinai

linear equations over noncommutative graded rings abstract we call a graded connected algebra r effectively coherent if for every linear equation over r with homogeneous coefficients of degrees at most d the degrees of generators of its module of solutions are bounded by some function d d for commutative polynomial rings this property has been established by hermann in 1926 we establish the same property for several classes of noncommutative algebras including the most common class of rings in noncommutative projective geometry that is strongly noetherian rings which includes noetherian pi algebras and sklyanin algebras we extensively study so called universally coherent algebras that is such that the function d d is bounded by 2d for d 0 for example finitely presented monomial algebras belong to this class as well as many algebras with finite groebner basis of relations

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

the universal enveloping algebra of the witt algebra is not noetherian abstract this work is prompted by the long standing question of whether it is possible for the universal enveloping algebra of an infinite dimensional lie algebra to be noetherian to address this problem we answer a 23 year old question of carolyn dean and lance small namely we prove that the universal enveloping algebra of the witt or centerless virasoro algebra is not noetherian to show this we prove our main result the universal enveloping algebra of the positive part of the witt algebra is not noetherian we employ algebro geometric techniques from the first author s classification of noncommutative birationally commutative projective surfaces as a consequence of our main result we also show that the enveloping algebras of many other infinite dimensional lie algebras are not noetherian these lie algebras include the virasoro algebra and all infinite dimensional z graded simple lie algebras of polynomial growth

representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities we give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products with parameter t 0 and the derived category of coherent sheaves on a crepant resolution of the spectrum of the centre of these algebras

calogero moser space and kostka polynomials abstract we consider the canonical map from the calogero moser space to symmetric powers of the affine line sending conjugacy classes of pairs of n n matrices to their eigenvalues we show that the character of a natural c action on the scheme theoretic zero fiber of this map is given by kostka polynomials a similar result is proved for a cyclic version of the calogero moser space

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

naive blowups and canonical birationally commutative factors in 2008 rogalski and zhang math z 259 2 433 455 2008 showed that if r is a strongly noetherian connected graded algebra over an algebraically closed field bbbk then r has a canonical birationally commutative factor this factor is up to finite dimension a twisted homogeneous coordinate ring b x mathcal l sigma here x is the projective parameter scheme for point modules over r as well as tails of points in mathrm qgr r as usual sigma is an automorphism of x and mathcal l is a sigma ample invertible sheaf on x we extend this result to a large class of noetherian but not strongly noetherian algebras specifically let r be a noetherian connected graded bbbk algebra where bbbk is an uncountable algebraically closed field let y infty denote the parameter space or stack or proscheme parameterizing r point modules and suppose there is a projective variety x that corepresents tails of points there is a canonical map p y infty rightarrow x if the indeterminacy locus of p 1 is 0 dimensional and x satisfies a mild technical assumption we show that there is a homomorphism g r rightarrow b x mathcal l sigma and that g r is up to finite dimension a naive blowup on x in the sense of keeler et al duke math j 126 3 491 546 2005 rogalski and stafford j algebra 318 2 794 833 2007 and satisfies a universal property we further show that the point space y infty is noetherian

the noncommutative schemes of generalized weyl algebras abstract the first weyl algebra over k a 1 k x y x y y x 1 admits a natural z grading by letting deg x 1 and deg y 1 smith showed that gr a 1 is equivalent to the category of quasicoherent sheaves on a certain quotient stack using autoequivalences of gr a 1 smith constructed a commutative ring c graded by finite subsets of the integers he then showed gr a 1 gr c z fin in this paper we prove analogues of smith s results by using autoequivalences of a graded module category to construct rings with equivalent graded module categories for certain generalized weyl algebras we use autoequivalences defined in a companion paper so that these constructions yield commutative rings

germs of arcs on singular algebraic varieties and motivic integration we study the scheme of formal arcs on a singular algebraic variety and its images under truncations we prove a rationality result for the poincare series of these images which is an analogue of the rationality of the poincare series associated to p adic points on a p adic variety the main tools which are used are semi algebraic geometry in spaces of power series and motivic integration a notion introduced by m kontsevich in particular we develop the theory of motivic integration for semi algebraic sets of formal arcs on singular algebraic varieties we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of oesterle

numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides the wave and finite element wfe method is a numerical approach to the calculation of the wave properties of structures of arbitrary complexity the method starts from a finite element fe model of only a short segment of the structure typically by using existing element libraries and commercial fe packages the dynamic stiffness matrix of the segment is obtained a periodicity condition applied and an eigenvalue problem formed whose solution gives the dispersion equations and wave mode shapes these define a wave basis from which the forced response can be found straightforwardly although straightforward in application the wfe method is prone to numerical difficulties these are discussed in this paper and methods to avoid or remove them described attention is focused on 1 dimensional waveguide structures for which numerical problems are most severe three ways of phrasing the eigenvalue problem for free wave propagation are presented and a method based on singular value decomposition is proposed to determine eigenvectors at low frequencies discretisation errors are seen to occur if the segment is too large while round off errors occur if the segment is too small this can be overcome by forming a super segment from the concatenation of two or more segments the forced response is then considered the use of a reduced wave basis removes many problems direct calculation of the waves excited by a point force is very prone to poor numerical conditioning but can be circumvented by exploiting the orthogonality of the left and right eigenvectors numerical examples are presented

dynamic modelling of railway track a periodic model based on a generalized beam formulation abstract dynamic modelling of railway track is a vital step in view of traffic noise reduction considering the track as a periodic structure the classical properties and methods associated with one dimensional periodic structures are recalled then applied to the problem within the framework of the euler bernouilli and timoshenko beam theories these methods turn out to be insufficient when compared with experimental data especially concerning the lateral receptance spectrum therefore an extended beam model is developed essentially based on the notion of generalized cross section displacements finally the application of this theory to railway track results in a significant improvement in the computed spectrum and suggests directions for further investigations

geometric algebras on projective surfaces abstract let x be a projective surface let aut x and let l be a ample invertible sheaf on x we study the properties of a family of subrings parameterized by geometric data of the twisted homogeneous coordinate ring b x l in particular we find necessary and sufficient conditions for these subrings to be noetherian we also study their homological properties their associated noncommutative projective schemes and when they are maximal orders in the process we produce new examples of maximal orders these are graded and have the property that no veronese subring is generated in degree 1 our results are used in the companion paper s j sierra 2009 sie09 to give defining data for a large class of noncommutative projective surfaces

rational cherednik algebras and hilbert schemes let h c be the rational cherednik algebra of type a n 1 with spherical subalgebra u c e h c e then u c is filtered by order of differential operators with associated graded ring mbox gr u c mathbb c mathfrak h oplus mathfrak h where w is the n th symmetric group we construct a filtered mathbb z algebra b such that under mild conditions on c the category b qgr of graded noetherian b modules modulo torsion is equivalent to u c mod the associated graded mathbb z algebra mbox gr b has mbox gr b lqgr simeq coh hilb n this can be regarded as saying that u c simultaneously gives a non commutative deformation of mathfrak h oplus mathfrak h w and of its resolution of singularities hilb n rightarrow mathfrak h oplus mathfrak h as we show elsewhere this result is a powerful tool for studying the representation theory of h c and its relationship to hilb n

on intrinsic randomness of dynamical systems we discuss the problem of nonunitary equivalence via positivity preserving similarity transformations between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes dynamical systems admitting such nonunitary equivalence with stochastic markov processes are said to beintrinsically random in a previous work it was found that the so called bernoulli systems discrete time are intrinsically random in this sense this result is extended here by showing that a more general class of dynamical systems the so calledk systems andk flows are intrinsically random the connection of intrinsic randomness with local instability of motion is briefly discussed we also show that markov processes associated through nonunitary equivalence tononisomorphic k flows are necessarily non isomorphic

homological aspects of noetherian pi hopf algebras and irreducible modules of maximal dimension abstract we prove that a noetherian hopf algebra of finite global dimension possesses further attractive homological properties at least when it satisfies a polynomial identity this applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity as well as to classical enveloping algebras in positive characteristic in all three cases we show that these algebras are auslander regular and macaulay we derive representation theoretic consequences concerning the coincidence of the non azumaya and singular loci for each of the above three classes of algebras

entropy functionals associated to shifts dynamical systems abstract we construct entropy functionals which discriminate the measures which converge to equilibrium in the case of shifts dynamical systems in particular for k shifts it is proved that some functionals associated to them decrease monotonically to zero

generic noncommutative surfaces abstract we study a class of noncommutative surfaces and their higher dimensional analogs which come from generic subalgebras of twisted homogeneous coordinate rings of projective space such rings provide answers to several open questions in noncommutative projective geometry specifically these rings r are the first known graded algebras over a field k which are noetherian but not strongly noetherian in other words r k b is not noetherian for some choice of commutative noetherian extension ring b this answers a question of artin small and zhang the rings r are also maximal orders but they do not satisfy all of the conditions of artin and zhang in particular they satisfy the 1 condition but not i for i 2 answering a question of stafford and zhang and a question of stafford and van den bergh finally we show that the noncommutative scheme r proj has finite global dimension

naive noncommutative blowups at zero dimensional schemes abstract in an earlier paper d s keeler d rogalski j t stafford naive noncommutative blowing up duke math j 126 2005 491 546 mr 2120116 we defined and investigated the properties of the naive blowup of an integral projective scheme x at a single closed point in this paper we extend those results to the case when one naively blows up x at any suitably generic zero dimensional subscheme z the resulting algebra a has a number of curious properties for example it is noetherian but never strongly noetherian and the point modules are never parametrized by a projective scheme this is despite the fact that the category of torsion modules in qgr a is equivalent to the category of torsion coherent sheaves over x these results are used in the companion paper d rogalski j t stafford a class of noncommutative projective surfaces in press to prove that a large class of noncommutative surfaces can be written as naive blowups

description of a class of markov processes equivalent tok shifts it results from recent works of prigogine and collaborators that one can construct a nonunitary operator which realizes an equivalence between the positive actions of a reversible dynamical system and an irreversible markov process going to equilibrium we consider here this construction and we prove that a fork shifts the transition probability of the associated markov process is concentrated in the stable manifold of the transformed point by the shift with a point mass concentrated on the deterministic trajectory and b for bernoulli shifts the measures which go to equilibrium are the same for the deterministic system and the markov process

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

deformations of algebras defined by tilting bundles abstract in this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles we do this in two settings first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformation of that scheme and then expanding this result to c equivariant deformations over schemes with a good c action in both these situations the endomorphism algebra of the lifted tilting bundle produces a deformation of the original endomorphism algebra and this is a graded deformation in the c equivariant case we apply our results to rational surface singularities generalising the deformed preprojective algebras of crawley boevey and holland and also to symplectic situations where the deformations produced are related to symplectic reflection algebras

modelling wave propagation in two dimensional structures using finite element analysis a method is described by which the dispersion relations for a two dimensional structural component can be predicted from a finite element fe model the structure is homogeneous in two dimensions but the properties might vary through the thickness this wave finite element wfe method involves post processing the mass and stiffness matrices found using conventional fe methods of a segment of the structure this is typically a 4 noded rectangular segment although other elements can be used periodicity conditions are applied to relate the nodal degrees of freedom and forces the wavenumbers real imaginary or complex and the frequencies then follow from various resulting eigenproblems the form of the eigenproblem depends on the nature of the solution sought and may be a linear quadratic polynomial or transcendental eigenproblem numerical issues are discussed examples of a thin plate an asymmetric laminated plate and a laminated foam cored sandwich panel are presented for the last two examples developing an analytical model is a formidable task at best the method is seen to give accurate predictions at very little computational cost furthermore since the element matrices are typically found using a commercial fe package the meshing capabilities and the wealth of existing element libraries can be exploited

noncommutative graded domains with quadratic growth letk be an algebraically closed field and letr be a finitely generated connected gradedk algebra which is a domain of gelfand kirillov dimension two write the graded quotient ringq r ofr asd z z 1 for some automorphism of the division ringd we prove thatd is a finitely generated field extension ofk of transcendence degree one moreover we describer in terms of geometric data ifr is generated in degree one then up to a finite dimensional vector space r is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curvey this implies in particular thatr is noetherian thatr is primitive when and thatr is a finite module over its centre when ifr is not generated in degree one thenr will still be noetherian and primitive if has infinite order butr need not be noetherian when has finite order

idealisers in skew group rings abstract let c be a commutative noetherian domain g be a finitely generated abelian group which acts on c and b c g be the skew group ring for a prime ideal i c we study the largest subring of b in which the right ideal ib becomes a two sided ideal the idealiser subring we obtain necessary and sufficient conditions for when this idealiser subring is left and right noetherian we also give an example of these conditions in practice which translates to an interesting number theoretic problem

non commutative resolutions of quotient singularities for reductive groups in this paper we generalize standard results about non commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups we show in particular that quotient singularities for reductive groups always have non commutative resolutions in an appropriate sense moreover we exhibit a large class of such singularities which have twisted non commutative crepant resolutions we discuss a number of examples both new and old that can be treated using our methods notably we prove that twisted non commutative crepant resolutions exist in previously unknown cases for determinantal varieties of symmetric and skew symmetric matrices in contrast to almost all prior results in this area our techniques are algebraic and do not depend on knowing a commutative resolution of the singularity

wave propagation along transversely periodic structures the dispersion curves for guided waves have been of constant interest in the last decades because they constitute the starting point for nde ultrasonic applications this paper presents an evolution of the semianalytical finite element method and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation this method allows a complete investigation of the dispersion curves and of displacement stress fields for guided modes in anisotropic and absorbing periodic structures among other examples that of a grooved aluminum plate is theoretically and experimentally investigated indicating the presence of specific and original guided modes

symplectic random vibration analysis of a vehicle moving on an infinitely long periodic track based on the pseudo excitation method pem symplectic mathematical scheme and schur decomposition the random responses of coupled vehicle track systems are analyzed the vehicle is modeled as a spring mass damper system and the track is regarded as an infinitely long substructural chain consisting of three layers i e the rails sleepers and ballast the vehicle and track are coupled via linear springs and the moving vehicle model is adopted the latter assumes that the vehicle moves along a static track for which the rail irregularity is further assumed to be a zero mean valued stationary gaussian random process the problem is then solved efficiently as follows initially pem is used to transform the rail random excitations into deterministic harmonic excitations the symplectic mathematical scheme is then applied to establish a low degree of freedom equation of motion with periodic coefficients in turn these are transformed into a linear equation set whose upper triangular coefficient matrix is established using the schur decomposition scheme finally the frequency dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo excitations the proposed method is subsequently justified by comparison with a monte carlo simulation the fixed vehicle model and the moving vehicle model are compared and the influences of vehicle velocity and class of track on system responses are also discussed

cohomology of schematic algebras letrbe a positively graded noetheriank algebra and let proj r r grbe the quotient category of the category of gradedr modulesr grmodulo those of finite length ifris schematic cf f van oystaeyen and l willaert j pure appl algebra104 1995 109 122 and has finite global dimension we show that the cohomology groups ofr as defined in m artin and j j zhang adv in math 109 1994 228 287 are finite dimensional furthermore we introduce cech cohomology groups for schematic algebras and prove that they coincide with the usual graded cohomology groups these generalized cech cohomology groups are still manageable we illustrate this with an example

on wave propagation in repetitive structures two forms of transfer matrix abstract two forms of dynamic transfer matrix are derived for a one dimensional beam like repetitive pin jointed structure with point masses located at nodal cross sections the displacement force transfer matrix g and the displacement displacement transfer matrix h similarity matrices are introduced to relate g and h together with their respective metrics symplectic orthogonality relationships for the eigenvectors of both g and h are derived together with relationships between their respective sets of eigenvectors new expressions for the group velocity are derived for repetitive structures of finite length natural frequency equations are derived employing both g and h including phase closure and the direct application of boundary end conditions besides an exposition of the theory some familiar but much new the focus of the present paper is on the relationships between the two forms of transfer matrix including their respective dis advantages numerical results together with further theory necessary for interpretation are presented in companion papers

naive noncommutative blowing up let b x mathscr l be the twisted homogeneous coordinate ring of an irreducible variety x over an algebraically closed field k with dim x 2 assume that c in x and in aut x are in sufficiently general position we show that if one follows the commutative prescription for blowing up x at c but in this noncommutative setting one obtains a noncommutative ring r r x c mathscr l with surprising properties 1 r is always noetherian but never strongly noetherian 2 if r is generated in degree one then the images of the r point modules in qgr r are naturally in one to one correspondence with the closed points of x however in both qgr r and gr r the r point modules are not parametrized by a projective scheme 3 while qgr r has finite cohomological dimension dim k h 1 mathscr o

on the forced response of waveguides using the wave and finite element method the forced response of waveguides subjected to time harmonic loading is treated the approach starts with the wave and finite element wfe method where a segment of the waveguide is modeled using traditional finite element methods the mass and stiffness matrices of the segment are used to formulate an eigenvalue problem whose solution yields the wave properties of the waveguide the wfe formulation is used to obtain the response of the waveguide to a convected harmonic pressure chp since the fourier transform of the response to a general excitation is a linear combination of the responses to chps the response to a general excitation can be obtained via an inverse fourier transform process this is evaluated analytically using contour integration and the residue theorem hence the approach presented herein enables the response of a waveguide to general loading to be found by a modeling a segment of the waveguide using finite element methods and post processing it to obtain the wave characteristics b using fourier transform and contour integration to obtain the wave amplitudes and c using the wave amplitudes to find the response at any point in the waveguide numerical examples are presented

geometric idealizer rings let b b x be the twisted homogeneous coordinate ring of a projective variety x over an algebraically closed field k we construct and investigate a large class of interesting and highly noncommutative noetherian subrings of b specifically let z be a closed subscheme of x and let i b be the corresponding right ideal of b we study the subalgebra r k i of b under mild conditions on z and aut k x r is the idealizer of i in b the maximal subring of b in which i is a two sided ideal our main result gives geometric conditions on z and that determine the algebraic properties of r we say that n z is critically transverse if for any closed subscheme y of z for n 0 the sub schemes y and n z are homologically transverse we show that if n z is critically transverse then r is left and right noetherian has finite left and right cohomological dimension is strongly right noetherian but not strongly left noetherian and satisfies right d where d codim z but fails left 1 this generalizes results of rogalski in the case that z is a point in d we also give an example of a right noetherian ring with infinite right cohomological dimension partially answering a question of stafford and van den bergh further we study the geometry of critical transversality and show that it is often generic behavior in a sense that we make precise

canonical maps to twisted rings if a is a strongly noetherian graded algebra generated in degree one then there is a canonically constructed graded ring homomorphism from a to a twisted homogeneous coordinate ring open image in new window which is surjective in large degree this result is a key step in the study of projectively simple rings the proof relies on some results concerning the growth of graded rings which are of independent interest

homological properties of graded noetherian pi rings abstract let r be a connected graded noetherian pi ring if injdim r n r is auslander gorenstein and cohen macaulay with gelfand kirillov dimension equal to n if gldim r n r is a domain finitely generated as a module over its centre and a maximal order in its quotient division ring similar results hold if r is assumed to be local rather than connected graded alternatively suppose that r is a noetherian pi ring with gldim r r m 1 hd r m 2 for any two maximal ideals m i in the same clique then r is a direct sum of prime rings is integral over its centre and is auslander gorenstein if r is a prime ring then the centre z r of r is a krull domain and r equals its trace ring tr moreover hd r m height m for every maximal ideal m of r

the forced vibration of one dimensional multi coupled periodic structures an application to finite element analysis abstract a general theory for the forced vibration of multi coupled one dimensional periodic structures is presented as a sequel to a much earlier general theory for free vibration starting from the dynamic stiffness matrix of a single multi coupled periodic element it derives matrix equations for the magnitudes of the characteristic free waves excited in the whole structure by prescribed harmonic forces and or displacements acting at a single periodic junction the semi infinite periodic system excited at its end is first analysed to provide the basis for analysing doubly infinite and finite periodic systems in each case total responses are found by considering just one periodic element an already known method of reducing the size of the computational problem is reexamined expanded and extended in detail involving reduction of the dynamic stiffness matrix of the periodic element through a wave coordinate transformation use of the theory is illustrated in a combined periodic structure finite element analysis of the forced harmonic in plane motion of a uniform flat plate excellent agreement between the computed low frequency responses and those predicted by simple engineering theories validates the detailed formulations of the paper the primary purpose of the paper is not towards a specific application but to present a systematic and coherent forced vibration theory carefully linked with the existing free wave theory