inclusion principle for the rayleigh ritz based substructure synthesis according to this substructure synthesis the motion of every substructure is modeled in terms of quasicomparison functions which are linear combinations of admissible functions capable of satisfying all the boundary conditions

reduction of substructural interface degrees of freedom in flexibility based component mode synthesis a flexibility based component mode synthesis cms is proposed for reduced order modelling of dynamic behaviour of large structures the approach employs partitioning via the localized lagrange multiplier method the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes the flexibility based cms method has shown significant advantages over the classical craig bampton method a key feature of the method is its substructural mode selection criterion that is independent of loading conditions unlike the majority of available cms approaches where one retains the full dimension of partition boundary degrees of freedom dofs the flexibility based method allows to reduce significantly the interface dofs the reduction of interface dofs represents the major contribution of the present communication the efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3d structure both partitioned into several substructures copyright 2006 john wiley sons ltd

rayleigh ritz based substructure synthesis for flexible multibody systems this paper is concerned with the modeling of flexible multibody systems by a rayleigh ritz based substructure synthesis method so that certain advantages can be accrued by using the variational approach to derive the eigenvalue problem as with the classical rayleigh ritz method if the admissible functions used to represent the motion of the substructures are not chosen properly convergence can suffer this paper presents a new substructure synthesis method with superior convergence characteristics achieved by representing the motion by means of a recently developed class of functions namely the class of quasi compari son functions this improved convergence is shown to be related to improved approximation of both the differential equations and the natural boundary conditions the theory is demonstrated by means of a numerical example i introduction t his investigation is concerned with the modeling of flexible multibody systems many structures such as fixedwing aircraft helicopters flexible spacecraft flexible robots etc can be modeled as assemblages of interacting flexible bodies a method proposed by hurty1 2 in the early 1960s and known as component mode synthesis consists of modeling the motion of the individual substructures referred to as components by means of component modes he uses three types of modes to represent the motion of a substructure rigid body modes constraint modes and normal modes to define constraint modes hurty divides the constraints into two classes statically determinate and redundant the constraint modes are equal in number to the number of redundant constraints and are defined by producing a unit displacement on each redundant constraint in turn with all other constraints fixed the normal modes represent the modes of vibration of the components with all constraints fixed an approach by craig and hampton3 differs from that of hurty 1 2 mainly in the selection of the component modes indeed craig and hampton suggest two types of component modes boundary modes providing for displacements and rotations at points along the substructure boundaries and related to the constraint modes of hurty and substructure modes corresponding to completely restrained boundaries the substructures modeled individually in refs 1 3 are made to act together as a single structure by eliminating the redundant generalized coordinates arising from the fact that displacements at points common to two adjacent substructures are included twice in the overall problem formulation once for each substructure the elimination process is based on the use of constraint equations resulting from the enforcement of compatibility conditions which amounts to saying that the displacement of a boundary point shared by two substructures is the same in another approach to the problem proposed by

the center of the enveloping algebra of the p lie algebras n n n when p divides n abstract let be a reductive lie algebra over an algebraically closed field f with char f p 0 suppose g satisfies jantzen s standard assumptions then the structure of z the center of the enveloping algebra is described by the extended veldkamp s theorem we examine here the deviation of z from this theorem in case or and p n it is shown that veldkamp s description is valid for this implies that friedlander parshall donkin decomposition theorem for holds in case p is good for a semi simple simply connected g excluding if p 2 a 1 factors of g in case or we prove a fiber product theorem for a polynomial extension of z however veldkamp s description mostly fails for and in particular z is not cohen macaulay if n 4 in both cases contrary to a result of kac weisfeiler we show for an odd prime p that and do not generate we also show for that the codimension of the non azumaya locus of z is at least 2 if n 3 and exceeds 2 if n 4 this refutes a conjecture of brown goodearl we then show that z is factorial excluding thus confirming a conjecture of premet tange we also verify humphreys conjecture on the parametrization of blocks in case p is good for g

centers of reduced enveloping algebras we compute the inverse image of a functional in the zassenhaus variety we apply this computation to describe the category of representations for a regular functional

a general procedure for improving substructures representation in dynamic synthesis in the general substructure synthesis method for the dynamic analysis of complex flexible structures developed earlier by the authors the motion of each substructure is represented by a given number of substructure admissible functions and the otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of weighted residuals in this paper a general procedure for improving the admissible functions representing each substructure in the synthesis is developed the procedure is an iterative one and it leads to an improved eigensolution for the intermediate structure i e a fictitious structure defined by the approximate compatibility conditions where the improved eigensolution is obtained while always using the same number of degrees of freedom to represent a given substructure in any iteration the computations associated with each substructure are independent of those for all other substructures and they can be performed in parallel by increasing the number of iterations the eigensolution for the intermediate structure is approached the procedure is applicable to assembled structures that are either positive definite or positive semidefinite moreover the procedure represents an extension of the concept of subspace iteration to structures composed of substructures

model order reduction in hyperelasticity a proper generalized decomposition approach this paper deals with the extension of proper generalized decomposition methods to non linear problems in particular to hyperelasticity among the different approaches that can be considered for the linearization of the doubly weak form of the problem we have implemented a new one that uses asymptotic numerical methods in conjunction with proper generalized decomposition to avoid complex consistent linearization schemes necessary in newton strategies this approach results in an approximation of the problem solution in the form of a series expansion each term of the series is expressed as a finite sum of separated functions the advantage of this approach is the presence of only one tangent operator identical for every term in the series the resulting approach has proved to render very accurate results that can be stored in the form of a meta model in a very compact format this opens the possibility to use these results in real time reaching khz feedback rates or to be used in deployed handheld devices such as smartphones and tablets

a lean and efficient snapshot generation technique for the hyper reduction of nonlinear structural dynamics abstract model order reduction based on subspace projection can lead to impressive speedups as the number of dofs can be drastically reduced however the computation of the nonlinear forces which is performed in the unreduced physical domain becomes the dominating bottleneck for nonlinear systems this issue is addressed by hyper reduction which is the approximate but inexpensive computation of the nonlinear forces in a reduced basis model the established hyper reduction methods require training sets which are usually obtained by a training simulation of the full unreduced model resulting in immense offline costs to reduce the offline costs so called nonlinear stochastic krylov training sets nskts are proposed in this paper these training sets are obtained by solving a number of nonlinear static problems where the force is constructed by stochastically weighted forces of a krylov force subspace the feasibility of nskts as training sets for the energy conserving mesh sampling and weighting ecsw hyper reduction method is demonstrated on a geometrically nonlinear rubber boot example exhibiting excellent results in terms of accuracy speedup and robustness

completions of noetherian p i rings abstract let r be a left noetherian p i ring and m a maximal semimaximal ideal in r satisfying i m i 0 it is proven that r z lim i r m i the completion of r with respect to m i is left noetherian settling affirmatively a conjecture of goldie g however usually r is neither left nor right flat over r and height m height m

ideal arithmetic in noetherian pi rings a domain satisfying the above equivalent characterisations is called a dedekind domain in the setting of non commutative orders the corresponding theory was axiomatised by asano 2 31 and further relined by michler t l and robson 1131 the starting point of this theory is condition b and indeed in modern terms the rings considered by asano can be thought of as prime noetherian rings satisfying a polynomial identity and condition fb however while condition a is often taken to be the definition of a commutative dedekind domain 10 p 294 15 p 2701 its implications in non commutative rings have not so far been studied it is the aim of this paper to do so one obstruction to following one of the standard proofs of the commutative theory is that if p p 1 p is an invertible product of prime ideals then it is not immediately clear that each pi is individually 475 0021 8693 89 3 00

manifold reconnection and diffusion in strong chaos abstract we analyse diffusion across a reconnecting zone in a regime of strong chaos numerical estimates from the angular correlation functions averaged over a suitable set of phase space initial conditions are compared to a local diffusion coefficient obtained using fick s law it emerges that the diffusion coefficient is enhanced from small to larger values as successive reconnection like processes or more usual bifurcations take place this feature is illustrated using a quadratic nontwist map

a general dynamic synthesis for structures with discrete substructures abstract this paper presents a substructure synthesis method for the dynamic simulation of complex structures where the structures consist of an assemblage of discrete substructures an analogy between distributed and discrete structures is extensively invoked to stimulate the motion of discrete substructures the concept of admissible vectors is introduced where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures the individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures a numerical example illustrating the method is presented

dynamics of a two parameter family of maps of the interval on etudie la dynamique de la famille a 2 parametres des applications a une dimension x f x x 1 x x 0 1 ou les parametres et sont 0 et 1 on considere l effet de degres de liberte additionnels sur les varietes de comportement dynamique

nonlinear model order reduction based on local reduced order bases summary a new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced order bases is presented it is particularly suited for problems characterized by different physical regimes parameter variations or moving features such as discontinuities and fronts instead of approximating the solution of interest in a fixed lower dimensional subspace of global basis vectors the proposed model order reduction method approximates this solution in a lower dimensional subspace generated by most appropriate local basis vectors to this effect the solution space is partitioned into subregions and a local reduced order basis is constructed and assigned to each subregion offline during the incremental solution online of the reduced problem a local basis is chosen according to the subregion of the solution space where the current high dimensional solution lies this is achievable in real time because the computational complexity of the selection algorithm scales with the dimension of the lower dimensional solution space because it is also applicable to the process of hyper reduction the proposed method for nonlinear model order reduction is computationally efficient its potential for achieving large speedups while maintaining good accuracy is demonstrated for two nonlinear computational fluid and fluid structure electric interaction problems copyright 2012 john wiley sons ltd

on a new iterative approach of component mode synthesis a wholly new concept of intermediate structure is developed in this paper based on this a new component mode iteration cmi or subdomain subspace iteration method is proposed in the new cmi method the ordinarily required step of ensuring interface compatibility is eliminated an outstanding achievement of this method is that it retains the merit of the standard subspace iteration ssi technique concerning the number of vectors required in computation in the present method iteraton is carried out at subdomain levels on machines capable of parallel processing this work can be performed simultaneously numerical examples clearly demonstrate the excellence of this new method

asymptotic study of the elastic postbuckling behavior of structures by the finite element method abstract within the framework of finite element analysis an asymptotic method is presented for the study of geometrically nonlinear static behavior of thin structures under one parameter conservative loading the method can be applied when the prebuckling behavior is moderately non linear so that the bifurcation analysis is no longer accurate enough an iterative process makes it possible to find suitable deformation modes which enable a good approximation of the structural behavior around the buckling point as in the rayleigh ritz approach a reduced energy can be formulated with only a small number of generalized degrees of freedom the influence of small initial imperfections on the buckling load can easily be analyzed as in koiter s asymptotic method a comprehensive treatment and several improvements of this asymptotic iterative method are given and selected examples illustrate the basic features of the method

linear non linear dynamic substructures the dynamic substructure method is extended to linear and non linear coupling systems only those master co ordinates with non linear nature non linear co ordinates are retained other slave co ordinates relating to the linear part linear co ordinates are eliminated by the dynamic substructure method the dynamic flexibility matrix associated with the linear co ordinates is first expanded in terms of the fixed interface natural modes the condensed dynamic stiffness matrix associated with the non linear co ordinates is formed subsequently the convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and taylor series expansion to find the steady state solutions the non linear responses are expanded into a fourier series responses of the linear co ordinates are related to the non linear co ordinates analytically to solve for the unknown fourier coefficients the harmonic balance method gives a set of non linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients a newtonian algorithm is adopted to solve for the unknown fourier coefficients iteratively the computational cost of a non linear analysis depends heavily on the number of degrees of freedom encountered in the method the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced

the ramification of centres lie algebras in positive characteristic and quantised enveloping algebras let h be a hopf algebra over the field k which is a finite module over a central affine sub hopf algebra r examples include enveloping algebras u mathfrak g of finite dimensional k lie algebras mathfrak g in positive characteristic and quantised enveloping algebras and quantised function algebras at roots of unity the ramification behaviour of the maximal ideals of z h with respect to the subalgebra r is studied and the conclusions are then applied to the cases of classical and quantised enveloping algebras in the case of u mathfrak g for mathfrak g semisimple a conjecture of humphreys 28 on the block structure of u mathfrak g is confirmed in the case of u epsilon mathfrak g for mathfrak g semisimple and epsilon an odd root of unity we obtain a quantum analogue of a result of mirkovic and rumynin 35 and we fully describe the factor algebras lying over the regular sheet 9 the blocks of u epsilon mathfrak g are determined and a necessary condition which may also be sufficient for a baby verma u epsilon mathfrak g module to be simple is obtained

factoriality for the reductive zassenhaus variety and quantum enveloping algebra let u g be the enveloping algebra of a finite dimensional reductive lie algebra g over an algebraically closed field of prime characteristic let u p s be the simply connected quantum enveloping algebra at the root of unity of a complex semi simple finite dimensional lie algebra s we show by similar proofs that the centers of both are factorial while the first result was established by r tange 32 by different methods the second one confirms a conjecture in 4 we also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic

damped dynamic substructures the dynamic substructure method is extended to lightly or heavily damped systems both internal and external dampings are considered the damped dynamic flexibility associated with the slave co ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co ordinates is formed subsequently the convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices since the dynamic stiffness method is equivalent to the modal synthesis method the component mode method and kron s method the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices

dimensional model reduction in non linear finite element dynamics of solids and structures a general approach to the dimensional reduction of non linear finite element models of solid dynamics is presented for the newmark implicit time discretization the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments to deal with this it is shown how the problem can be formulated in an approximation ritz basis of much smaller dimension similarly the explicit newmark algorithm can be also written in a reduced dimension basis and the computation time savings in that case follow from an increase in the stable time step length in addition the empirical eigenvectors are proposed as the basis in which to expand the incremental problem this basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense because of this global time viewpoint the basis need not be updated as with reduced bases computed from a linearization of the full finite element model if the dynamics of a finite element model is expressed in terms of a small number of basis vectors the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved at the same time numerical experiments indicate that by using reduced models substantial savings can be achieved even in the pre asymptotic range furthermore the algorithm parallelizes very efficiently the method we present is expected to become a useful tool in applications requiring a large number of repeated non linear solid dynamics simulations such as convergence studies design optimization and design of controllers of mechanical systems

reduction method for finite element nonlinear dynamic analysis of shells doi 10 2514 1 j051003theprojectionoftheequationsofmotiononasuitablemodalbasiscandrasticallyreducethenumberofdegreesoffreedom of a nonlinear dynamic nite element analysis a reduction method based on enriching a set of vibrationmodeswithsecond ordermodescalculatedviaaperturbationtechniqueispresented thesesecond ordermodesarereadily calculated via the solution of corresponding linear problems the results indicate that the second ordermodes are displacement elds that are essential for an appropriate representation of the nonlinear behavior of thestructure problems exhibiting strong geometrical nonlinearities under relatively high dynamic loads aresuccessfully handled by forming the reduction basis with vibration modes and their corresponding second ordermodes calculated at two different static equilibrium con gurations

the centre of quantum sln at a root of unity abstract it is proved that the centre z of the simply connected quantised universal enveloping algebra over c u e p sl n e a primitive l th root of unity l an odd integer 1 has a rational field of fractions furthermore it is proved that if l is a power of an odd prime z is a unique factorisation domain

one dimensional dynamics for traveling fronts in coupled map lattices multistable coupled map lattices typically support traveling fronts separating two adjacent stable phases we show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one dimensional circle homeomorphism whose rotation number gives the propagation velocity the mode locking of the velocity with respect to the system parameters then typically follows we study the behavior of fronts near the boundary of parametric stability and we explain how the mode locking tends to disappear as we approach the continuum limit of an infinite density of sites

projective modules over the gerasimov sakhaev counterexample abstract we investigate the structure of the so called gerasimov sakhaev counterexample which is a particular example of a universal localization and classify both finitely and infinitely generated projective modules over it

model reduction to spectral submanifolds and forced response calculation in high dimensional mechanical systems abstract we show how spectral submanifold ssm theory can be used to extract forced response curves without any numerical simulation in high degree of freedom periodically forced mechanical systems we use multivariate recurrence relations to construct the ssms achieving a major speed up relative to earlier autonomous ssm algorithms the increase in computational efficiency promises to close the current gap between studying lower dimensional academic examples and analyzing larger systems obtained from finite element modeling as we illustrate on two different discretized damped forced beam models using the exact reduction procedure via ssms for obtaining forced response curves we further demonstrate speed gains of several orders in magnitude relative to the available state of the art continuation packages while retaining accuracy

prediction condensed models adapted to the nonlinear structures in time domain abstract this paper deals with a method to study closely the stationary solution of nonlinear dynamic systems in time domain this method is based on the exploitation of karhunen loeve decomposition with or without parametric modifications as well as on the characteristics of localized nonlinearities with the application of this method at first on linear models initially condensed by karhunen loeve the predictions of nonlinear responses can be obtained rapidly this method is adapted to a condensed linear model used in the first optimization procedure of the nonlinear dynamic behaviour this robust basis will be used as condensation basis of the modified model local per zone which leads to a prediction of vibratory responses of complex structures modified and affected by localized nonlinearities

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

classical localizability in solvable enveloping algebras and poincare birkhoff witt extensions abstract in several classes of noncommutative noetherian rings jategaonkar s intersection conditions are verified for finite unions of cliques of prime ideals and it follows that these finite unions of cliques are classically localizable if they satisfy incomparability among the rings in question are the enveloping algebra of any finite dimensional solvable lie algebra g over any field k of characteristic zero any twisted smash product r u g where r is a commutative noetherian k algebra and g acts on r via k linear derivations and certain iterated differential operator rings over r in contrast to previously verified cases k is allowed to be countable one tool used here a lying over theorem for cliques has some independent interest namely if r s is a flat finite centralizing extension of noetherian rings satisfying the second layer condition and if x is a clique in spec r there exists a clique y in spec s such that p r p y x

three dimensional flops and noncommutative rings limburgs univ ctr dept math b 3590 diepenbeek belgium van den bergh m limburgs univ ctr dept math univ campus b 3590 diepenbeek belgium vdbergh luc ac be

homological integral of hopf algebras the left and right homological integrals are introduced for a large class of infinite dimensional hopf algebras using the homological integrals we prove a version of maschke s theorem for infinite dimensional hopf algebras the generalization of maschke s theorem and homological integrals are the keys to studying noetherian regular hopf algebras of gelfand kirillov dimension one

on the use of modal derivatives for nonlinear model order reduction summary modal derivative is an approach to compute a reduced basis for model order reduction of large scale nonlinear systems that typically stem from the discretization of partial differential equations in this way a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller based on the resulting small scale state space model we investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction which has been missing so far concentrating on the application field of structural mechanics and structural dynamics we show that the concept of modal derivatives can also be applied as nonlinear extension of the craig bampton family of methods for substructuring we furthermore generalize the approach from a pure projection scheme to a novel reduced order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables this complexity reduction leads to a frequency preserving nonlinear quadratic state space model numerical examples with carefully chosen nonlinear model problems and three dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods along with the current limitations copyright 2016 john wiley sons ltd

an investigation of the convergence to the stationary state in the hassell mapping abstract we investigate the convergence to the fixed point and near it in a transcritical bifurcation observed in a hassell mapping we considered a phenomenological description which was reinforced by a theoretical description at the bifurcation we confirm the convergence for the fixed point is characterized by a homogeneous function with three exponents near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law although the expression of the mapping is different from the traditional logistic mapping at the bifurcation and near it the local dynamics is essentially the same for either mappings

partitioned component mode synthesis via a flexibility approach a new flexibility based component mode synthesis method is presented which is derived by approximating the partitioned equations of motion that employ a localized method of lagrange multipliers the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes hence the resulting interface flexibility matrices are uniquely determined and well suited for the present method development an attractive feature of the present method is its substructural mode selection criterion that is independent of loading conditions numerical experiments show that the present modal selection criterion is reliable and that the proposed flexibility based component mode synthesis method performs well relative to the classical craig bampton method in terms of accuracy and of its ability to include dominant substructural modes for simple plates and a relatively complex solid ring

substructure synthesis and its iterative improvement for large nonconservative vibratory systems a general synthesis method is developed for the dynamic analysis of nonconservati ve vibratory systems composed of substructures the idea of the synthesis is to represent each substructure by a reduced order model and to couple the substructure models together to act as the whole system for general nonconservative systems a state space formulation is adopted for each substructure reduced order substructure models are obtained by approximating each state vector as a linear combination of a small number of real trial vectors the accuracy with which the synthesized model represents the whole system depends on the choices of trial vectors and the number of vectors used a procedure is developed for increasing the accuracy by iteratively generating improved substructure trial state vectors

the zassenhaus variety of a reductive lie algebra in positive characteristic let g be the lie algebra of a connected reductive group g over an algebraically closed field k of characteristic p 0 let z be the centre of the universal enveloping algebra u u g of g its maximal spectrum is called the zassenhaus variety of g we show that under certain mild assumptions on g the field of fractions frac z of z is g equivariantly isomorphic to the function field of the dual space g with twisted g action in particular frac z is rational this confirms a conjecture of j alev furthermore we show that z is a unique factorisation domain confirming a conjecture of a braun and c hajarnavis recently a premet used the above result about frac z a result of colliot thelene kunyavskii popov and reichstein and reduction mod p arguments to show that the gelfand kirillov conjecture cannot hold for simple complex lie algebras that are not of type a c or g2

dynamic analysis using a reduced basis of exact modes and ritz vectors the problem of obtaining an approximate solution for the response of a structure under dynamic forces is addressed the structure is modeled using mass and stiffness matrices and has n degrees of freedom an dimensional approximation is sought in a subspace defined by an arbitrary m orthogonal array a residual vector which is smaller in magnitude the more accurate the approximation is derived the residual contains two terms one is the error involved representing the force vector in the subspace the other is smaller the better the array leads to m approximate solutions of the exact eigenproblem numerical experiments are performed using arrays that are combinations of exact eigenvectors and of ritz vectors in one case when 11 different 10 dimensional bases are used to approximate the solution of a 60 degree of freedom problem it is found that a root mean square measure of relative error is smallest for the basis formed using the 6 lowest exact eigenvectors plus 4 ritz vectors generated from the spatial distribution of the loading

irreducible representations of lie algebras of reductive groups and the kac weisfeiler conjecture letg be the lie algebra of a connected reductive groupg over an algebraically closed field of characteristicp 0 suppose thatg 1 is simply connected andp is good for the root system ofg ifp 2 suppose in addition thatg admits a nondegenerateg invariant trace form letv be an irreducible and faithfulg module withp character g it is proved in the paper that dimv is divisible byp1 2dim where stands for the orbit of under the coadjoint action ofg

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

some homological invariants of local pi algebras during the last several years artin jorgensen stafford yekutieli and others have generalized many homological results from the commutative case to the noncommutative connected graded case az sz1 jo1 jo2 ye in this paper we generalize some of those to the noncommutative local case our main interest is on noetherian local pi polynomial identity algebras though some results hold in a more general setting throughout a is an algebra over a base field k i is its jacobson radical and a0 a i if a0 is artinian a is called semilocal if a0 is a simple artinian algebra respectively a division algebra then a is called local respectively scalar local unless otherwise stated we are working with left modules and sometimes we use the term aop module for a right a module where aop is the opposite ring of a a finite a module means finitely generated over a we use noetherian respectively artinian for two sided noetherian respectively two sided artinian

a procedure for improving discrete substructure representation in dynamic synthesis n important problem in the dynamic analysis for flexible structures is that of determining the natural frequencies and associated natural modes of vibration particularly the lower ones complex structures are often represented by mathematical models such as finite element models possessing a very large number of degrees of freedom where the number can reach into the tens of thousands because of the large number of degrees of freedom a direct iterative method for obtaining a partial eigensolution know as subspace iteration was developed the subspace iteration method has a long history an extensive bibliography is given in ref 1 and the current status of the method is discussed in refs 2 4 in the context of structural dynamics even the subspace iteration method however can be overwhelmed by the large number of degrees of freedom in the mathematical model so that a method for prior reduction of the number of degrees of freedom is desirable complex structures are often modeled by breaking the structure into a number of simpler components or substructures the substructure models are then coupled together to form the whole structure model the technique is known as substructure synthesis and its origin can be found in refs 5 and 6 the idea of refs 5 and 6 is to represent the motion of each substructure by a set of substructure normal modes obtained by solving an eigenvalue problem for each substructure then each substructure is represented in the synthesis process by a reduced number of lower substructure modes the synthesis leads to an eigenvalue problem for the assembled structure of a substantially smaller order than that of the original formulation the price paid in reducing the order of the eigenvalue problem is that its solution is only an approximation of the actual eigensolution of the original structure

gelfand kirillov conjecture in positive characteristics abstract let g be a finite dimensional lie algebra over an algebraically closed field of characteristic p 0 and let u g be the universal enveloping algebra of g we show in this paper that the division ring of fractions of u g is isomorphic to the ring of fractions of a weyl algebra in the following cases for g gl n or sl n if p n for the witt algebra w 1 and for some tensor product w 1 a of w 1 with a truncated polynomial ring furthermore we also show that the centre of u g in the last two cases is a unique factorisation domain in accordance with recent results of premet tange braun and hajarnavis

on making large nonlinear problems small abstract a number of aspects of reduction methods for solution of large scale nonlinear problems are discussed including a selection of basis vectors for steady state problems b identification and determination of bifurcation and limit points and tracing post limit point and post bifurcation point paths using reduction methods c application of reduction methods to nonlinear problems with prescribed nonzero values of the field variable and d use of reduction methods in conjunction with multifield mixed finite element models four numerical examples are presented to demonstrate the effectiveness of using reduction methods for the solution of nonlinear thermal and structural problems also a number of research areas which have high potential for application of reduction methods are identified

manifold reconnection in chaotic regimes in this paper we extend the concept of separatrix reconnection into chaotic regimes we show that even under chaotic conditions one can still understand abrupt jumps of diffusive like processes in the relevant phase space in terms of relatively smooth realignments of stable and unstable manifolds of unstable fixed points

a homological reformulation of the link condition abstract we prove an equivalent condition for the existence of a link between prime ideals in terms of the structure of a certain cohomology module we use this formulation to answer an open question regarding the nature of module extensions over one sided noetherian rings we apply the techniques developed in this paper to the local link structure of prime ideals of small homological height and examine when certain noetherian rings satisfy the density condition

on the substructure synthesis method substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures the motion of each of the substructures is represented by a series of admissible functions vectors and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures because the series of admissible functions vectors represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions the computed eigensolution is only an approximation of the actual one convergence of computed eigenvalues to actual eigenvalues requires two limiting processes one in which the number of admissible functions vectors is increased and the other in which the number of geometric compatibility conditions is increased

localized discrete empirical interpolation method this paper presents a new approach to construct more efficient reduced order models for nonlinear partial differential equations with proper orthogonal decomposition and the discrete empirical interpolation method deim whereas deim projects the nonlinear term onto one global subspace our localized discrete empirical interpolation method ldeim computes several local subspaces each tailored to a particular region of characteristic system behavior then depending on the current state of the system ldeim selects an appropriate local subspace for the approximation of the nonlinear term in this way the dimensions of the local deim subspaces and thus the computational costs remain low even though the system might exhibit a wide range of behaviors as it passes through different regimes ldeim uses machine learning methods in the offline computational phase to discover these regions via clustering local deim approximations are then computed for each cluster in the online computational phase machine

solution of non linear thermal transient problems by a reduction method a new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described the basis of the subspace is formed by using the system response at the first time step or an approximation to it and a set of orthogonal vectors obtained by the algorithm of lanczos derivatives of these vectors are included when treating non linear cases the method allows one to handle the sharp gradients that appear in thermally loaded structures and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system the algorithm is specially well suited for treating large scale problems examples dealing with one two and three dimensional cases of linear and non linear conduction problems are presented

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

zassenhaus varieties of general linear lie algebras abstract let g be a lie algebra over an algebraically closed field of characteristic p 0 and let u g be the universal enveloping algebra of g we prove in this paper for g gl n and g sl n that the centre of u g is a unique factorisation domain and its field of fractions is rational for g sl n our argument requires the assumption that p n while for g gl n it works for any p it turned out that our two main results are closely related to each other the first one confirms in type a a recent conjecture of a braun and c hajarnavis while the second answers a question of j alev

a reduction method for nonlinear structural dynamic analysis abstract a computational algorithm for predicting the nonlinear dynamic response of a structure is presented the nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a rayleigh ritz analysis the basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing only a few basis updatings are required during the whole time integration the truncation error introduced at every change of basis is pointed out as the cause for a divergence type behaviour and some means for eliminating it are discussed results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations

synchronization in two layer bistable coupled map lattices abstract the dynamics of a two layer bistable coupled map lattice cml is investigated a methodology for the construction of invariant domains in the phase space is developed and applied to the study of pattern formation and inter layer synchronization sufficient conditions for global synchronization are obtained the phenomena of pattern interaction and replication of form is also investigated finally possible instabilities of the synchronization mode and on off diagonal attractors are analyzed

the failure of the artin rees property for the jacobson radical in prime noetherian rings abstract we provide an example of a prime noetherian ring whose jacobson radical fails to satisfy the artin rees ar property on either side the ring constructed is a finite module over its noetherian centre this settles a longstanding question

some remarkable degenerations of quantum groups we show that an irreducible representation of a quantized enveloping algebraue at a lth root of 1 has maximal dimension l n if the corresponding symplectic leaf has maximal dimension 2n the method of the proof consists of a construction of a sequence of degenerations ofue the last one being aq commutative algebrau e 2n this allows us to reduce many problems concerningue to that concerningu e 2n

substructure synthesis method for frequency response of viscoelastic structures the method of substructure synthesis previously applicable to undamped and viscously damped systems has been extended to systems with viscoelastic damping in hereditary integral form differential operator form and steady state corm based on a variational principle for symmetric systems the corresponding substructure synthesis method is formulated in the frequency domain each substructure is represented by a set of admissible trial vectors in the rayleigh ritz method eigenvectors of the corresponding undamped substructure and ritz vectors obtained by spatial discretization of admissible functions are recommended as trial vectors the traditional state space formulation is avoided by the proposed substructure synthesis method so that the approach is independent of the form of viscoelastic models the effectiveness of the proposed method in terms of reducing the size of final equations is illustrated through numerical examples

robust attractor of non twist systems abstract we present a new kind of one dimensional attractor which has not yet been predicted in the non linear dynamics theory we consider a non linear map which presents typical non twist manifestations as isochronous resonances and shearless torus it is known that this torus corresponds to a very sturdy barrier in the phase space of some area preserving systems we show that when dissipation is present in the system the shearless curve carries its robustness to the dissipative scenario it becomes a powerful attractor which we call shearless attractor which is persistent under the variation of the parameters and it exchanges its stability from chaotic to quasi periodic or vice versa depending on the set of parameters

model order reduction for hyperelastic materials in this paper we develop a novel algorithm for the dimensional reduction of the models of hyperelastic solids undergoing large strains unlike standard proper orthogonal decomposition methods the proposed algorithm minimizes the use of the newton algorithms in the search of non linear equilibrium paths of elastic bodies the proposed technique is based upon two main ingredients on one side the use of classic proper orthogonal decomposition techniques that extract the most valuable information from pre computed complete models this information is used to build global shape functions in a ritz like framework on the other hand to reduce the use of newton procedures an asymptotic expansion is made for some variables of interest this expansion shows the interesting feature of possessing one unique tangent operator for all the terms of the expansion thus minimizing the updating of the tangent stiffness matrix of the problem the paper is completed with some numerical examples in order to show the performance of the technique in the framework of hyperelastic kirchhoff saint venant and neo hookean solids

effects of local nonlinearity and basin size in the dynamics of lattices of bistable maps we investigate the propagation of bistable fronts in lattices of diusively and advectively coupled cubic and quartic bistable maps reporting the distribution of both stable states for asymmetric basins of attraction the main eects of basin symmetry and local nonlinearities are obtained by comparing distributions for cubic local dynamics with either symmetric or asymmetric basins of attraction with those obtained for quartic maps with asymmetric basins in addition we show how front velocities depend on the local parameter and diusion c

model order reduction for temperature dependent nonlinear mechanical systems a multiple scales approach abstract the thermal dynamics in thermo mechanical systems exhibits a much slower time scale compared to the structural dynamics in this work we use the method of multiple scales to reduce the thermo mechanical structural models with a slowly varying temperature distribution in a systematic manner in the process we construct a reduction basis that adapts according to the instantaneous temperature distribution of the structure facilitating an efficient reduction in the number of unknowns as a proof of concept we demonstrate the method on a range of linear and nonlinear beam examples and obtain a consistently better accuracy and reduction in the number of unknowns than the standard galerkin projection using a constant basis

on quasiperiodic travelling waves in coupled map lattices we investigate quasiperiodic travelling waves qtws in lattices of diffusively coupled logistic maps starting from the assumption that any spatial structure can be broken down into simpler elementary structures a classification scheme for qtws is introduced within this framework the phenomenon of discrete velocities is reviewed and further investigated in addition a new technique is proposed for predicting whether qtws can occur for given parameter values and which they might be