products in hochschild cohomology and grothendieck rings of group crossed products abstract we give a general construction of rings graded by the conjugacy classes of a finite group some examples of our construction are the hochschild cohomology ring of a finite group algebra the grothendieck ring of the drinfel d double of a group and the orbifold cohomology ring for a global quotient we generalize the first two examples by deriving product formulas for the hochschild cohomology ring of a group crossed product and for the grothendieck ring of an abelian extension of hopf algebras our results account for similarities in the product structures among these examples

clifford correspondence for finite dimensional hopf algebras abstract let b h be a crossed product algebra over an algebraically closed field with h a finite dimensional hopf algebra we give an explicit equivalence between the category of finite dimensional b h modules whose restriction to b is a direct sum of copies of a stable irreducible b module and the category of modules for a twisted product of h with the field this describes all finite dimensional irreducible b h modules containing a stable irreducible b submodule and thus generalizes the classical stable clifford correspondence for groups in case h is cocommutative we extend this correspondence to the nonstable case

reconstruction of space dependent potential and or damping coefficients in the wave equation in this paper nonlinear reconstructions of the space dependent potential and or damping coefficients in the wave equation from cauchy data boundary measurements of the displacement and the flux tension are investigated this is a very interesting and challenging nonlinear inverse coefficient problem with important applications in wave propagation phenomena the uniqueness and stability results that are revised and in some cases proved demonstrate an advancement in understanding the stability of the inverse coefficient problems however in practice the inverse coefficient identification problems under investigation are still ill posed since small random errors in the input data cause large errors in the output solution in order to stabilize the solution we employ the nonlinear tikhonov regularization method numerical reconstructions performed for the first time are presented and discussed to illustrate the accuracy and stability of the numerical solutions under finite difference mesh refinement and noise in the measured data

localization and ideal theory in noetherian strongly group graded rings abstract we study primality hypercentrality simplicity and localization and the second layer condition in skew groups rings and group graded rings we give necessary and sufficient conditions for the skew group ring of a torsion free nilpotent group to be a simple ring and if the coefficient ring is commutative we give necessary and sufficient conditions for the skew group ring of an abelian group to be simple our method involves showing certain group graded rings are hypercentral our main results show that if g is a polycyclic by finite group and r is an artinian ring or a commutative noetherian ring then a strongly g graded ring with base ring r satisfies the second layer condition we discuss consequences of this for localization in such rings

input forces estimation of beam structures by an inverse method an on line recursive inverse method to estimate the input forces of beam structures is presented the inverse method is based on the kalman filter and a recursive least squares algorithm the filter models the system dynamics in a linear set of state equations the state equations of the beam structures were constructed using the finite element method the practicability and accuracy of the estimation method were examined with numerical simulations from which the input forces of a cantilever beam with a lumped mass on the free end were estimated from the output responses in the numerical experiments the cantilever beam was subjected to five types of input forces i e sinusoidal triangular impulse rectangular impulse a series of impulses and random the simulation results show that the inverse method has an excellent performance to estimate the input forces of beam structural systems from the noisy measurements

a dynamic programming algorithm for input estimation on linear time variant systems a time domain input estimation algorithm for linear systems with general time varying parameters is developed the algorithm is an extension of an existing approach for time invariant state space models and several new features such as higher order input approximations and an extended time variant output relation including direct input influence are introduced numerical examples are given to illustrate the new features and show that the algorithm is valid in a general time variant setting in particular excellent results are obtained for an ill posed moving force identification problem with noise contaminated data treated with tikhonov regularization

heavily separable functors abstract prompted by an example related to the tensor algebra we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable we test this notion on several functors traditionally connected to the study of separability

an inverse non linear force vibration problem of estimating the external forces in a damped system with time dependent system parameters abstract an inverse non linear force vibration problem based on the iterative regularization method i e the conjugate gradient method cgm is used to estimate the unknown time dependent external forces in a damped system having time dependent system parameters by using the measured system displacement it is assumed that no prior information is available on the functional form of the unknown external forces in the present study thus it is classified as the function estimation in inverse calculation the accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements the numerical simulations are performed to test the validity of present algorithm by using different types of external forces and measurements results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses within a couple of seconds of cpu time at pentium ii 300 mhz pc

characterization of p schemes of prime cube order abstract let p be a prime let s be a non commutative p scheme of order p 3 and assume that s is not thin we prove that each closed subset of order p 2 of s is an elementary abelian p group we also construct non commutative schurian p schemes of order p 3

a noether skolem theorem for group graded rings abstract the classical noether skolem theorem gives conditions to determine if an automorphism or a derivation of a finite dimensional central simple algebra is inner the definition of inner has been extended to more general hopf algebra actions in this paper we study group gradings of central simple algebras and we give sufficient conditions for the grading to be inner this provides a partial answer to a question of j bergen and s montgomery

force identification of dynamic systems using genetic programming one obvious limitation of the traditional force identification techniques is that they are unable to obtain the explicit expression of the force moreover some techniques need both the displacement and velocity data of all freedoms and some need the markov parameters from numerical calculation or experimental test before the force identification can be carried out this paper presents a genetic programming gp based method for excitation force identification of dynamic systems to overcome these traditional methods disadvantages gp is employed as a search and optimization method to obtain the optimal if not the best force expression from the known dynamic response one obvious merit of the proposed method is that it can obtain the explicit expression of the unknown force another advantage is that it only needs the dynamic response data at one point i e displacement or velocity or acceleration of one freedom illustrative examples demonstrate that the gp based method is able to identify the excitation force of a single degree a three degree dynamic systems and a frame structure depicting its potential for force forecast problems

a monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure poisson equation this paper describes a new monolithic approach based on the fluid pressure poisson equation ppe to solve an interaction problem of incompressible viscous fluid and an elastic body the ppe is derived so as to be consistent with the coupled equation system for the fluid structure interaction fsi based on this approach we develop two kinds of efficient monolithic methods in both methods the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all other unknown variables are derived fully explicitly or partially explicitly the coefficient matrix of the ppe for the fsi becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties the arbitrary lagrangian eulerian ale method is employed for the fluid part in order to take into account the deformable fluid structure interface to demonstrate fundamental performances of the proposed approach the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding copyright 2005 john wiley sons ltd

group graded rings and duality we give an alternative construction of the duality between finite group actions and group gradings on rings which was shown by cohen and montgomery in 1 this duality is then used to extend known results on skew group rings to corresponding results for large classes of group graded rings finally we modify the construction slightly to handle infinite groups introduction in the first section we give an alternate construction of the duality between finite group actions and group gradings on rings which was shown by cohen and montgomery in 1 this duality is then used to extend results on skew group rings and their modules to corresponding results for large classes of groupgraded rings in the second section we modify the construction slightly to handle infinite groups and apply it to a theorem on prime and semiprime infinite crossed products i would like to thank my thesis advisor d s passman for his guidance and encouragement throughout the writing of this paper 1 finite group graded rings and the smash product let g be a multiplicative group an associative ring with identity is said to be g graded if 1 r e r x xec is a direct sum of additive subgroups r x with r x r y c r xy it follows that necessarily 1r e r 1 so that each r x is a unitary r l bimodule if r e r we write r x for the component of r in r x so that r exgcr x r is said to be strongly g graded if r x r y r xy for all x y e g throughout this section r is assumed to be g graded where g is a finite group with igi n let mc r denote the set of n x n matrices over r with the rows and columns indexed by the elements of g if a c mg r we write ax y for the entry in the x y position of a then if a 1 c mc r the matrix product a 8 is given by 2 x x y e xx zaz y z e c if u c g is any subset of g let r u ex eur x in particular r r g now suppose h c g is a subgroup of g we define r h c mc r by r h a e ms r ax y e r xhy l that is r h ex ygcr xhy l e x y where e x y is the matrix unit with 1r in the x y position and zeroes elsewhere note that r g mc r received by the editors september 27 1984 1980 mathematics subject classification primary 16a03 c 1985 american mathematical society 0002 9947 85 1 00 25 per page

duality theorems for graded algebras and coalgebras the concepts of smash product and smash coproduct have been proved to be extremely useful tools in the theory of graded rings and graded coalgebras and more recently in the theory of action and coactions of a hopf algebra on an algebra or on a coalgebra once these concepts were defined a natural question appeared how can the smash product resp the smash coproduct be related to a matrix algebra resp to a matrix w x coalgebra the answer is given by the duality theorems proved in 3 for w x graded rings and in 5 for graded coalgebras various duality theorems w x w x for algebras have been proved during the last ten years cf 2 or 10 the purpose of this paper is to study duality for the smash product resp the smash coproduct associated to a g set and a g graded ring resp a g graded coalgebra the mentioned smash product and smash coproduct w x w x w x have been constructed in 10 and 6 it is shown by an example in 12 that for a g graded ring r and a left g set a we do not have a duality

noetherian semigroup algebras abstract it is shown that a semigroup s is finitely generated whenever the semigroup algebra k s is right noetherian and has finite gelfand kirillov dimension or s is a malcev nilpotent semigroup if furthermore s is a submonoid of a finitely generated nilpotent by finite group g then k s is right noetherian if and only if k s is left noetherian or equivalently s satisfies the ascending chain condition on right left ideals the latter condition is completely described in terms of the structure of s in case g is a nilpotent group the quotient group h of s contains a normal subgroup f such that h f is abelian by finite and f s finally also prime goldie contracted semigroup algebras are described

generalized 2 cocycles of finite groups and maximal orders abstract letrbe a dedekind domain with quotient fieldkand letgbe a finite group let g g r 0 be a generalized 2 cocycle i e not necessarily taking its values in the units ofr and consider the generalized twisted group ringr g in this paper we derive criteria forr gto be a graded maximalr order resp a hereditaryr order or a maximalr order ink g

a maschke type theorem for doi hopf modules and applications abstract we prove a maschke type theorem for doi hopf modules a sufficient condition in order to have a maschke type property is that there exists a normalized integral map for the doi hopf datum in question the results are applied to graded modules and to yetter drinfel d modules as another application a characterization of cosemisimple coalgebras over a field is given

galois extensions for co frobenius hopf algebras abstract forhan infinite dimensional co frobenius hopf algebra over a fieldk andaanh comodule algebra the smash producta h ratis linked to the ring of coinvariantsacohby a morita context we use the morita setting to show that for co frobeniush equivalent conditions fora acohto be galois parallel the case ofhfinite dimensional

crossed product algebras defined by separable extensions abstract we generalize the classical construction of crossed product algebras defined by finite galois field extensions to finite separable field extensions by studying properties of rings graded by groupoids we are able to calculate the jacobson radical of these algebras we use this to determine when the analogous construction of crossed product orders yield azumaya maximal or hereditary orders in a local situation thereby we generalize results by haile larson and sweedler

fixed rings and integrality abstract in this note we offer some variants of a theorem of pare and schelter on integrality in matrix rings we use these to deduce that a ring r is integral over the fixed subring r g under the action of a finite abelian group g provided g r r we also obtain an integrality version of the bergman isaacs theorem

von neumann regularity of smash products associated with g set gradings abstract for a g graded ring r the problem of gr regularity i e von neumann regularity condition on homogeneous elements has been treated earlier see n st sescu and van oystaeyen 1982 11 once the concept of the smash product was introduced this problem has been resumed by several authors this paper is concerned with von neumann regularity of two smash products the smash product r g of the g graded ring r by the group g and the smash product r a of r by a finite left g set a the connections between the regularity of r a and the gr regularity of r are also investigated one consequence of our results is that the smash product r a is a von neumann regular ring if and only if the category g a r gr is regular in stenstrom s sense

the extended brauer quotient of n interior g algebras abstract in this note we generalize the extended brauer quotient defined by l puig and y zhou in 4 section 3 to the case of n interior g algebras where n is a normal subgroup of a finite group g we use this extended brauer quotient on permutation algebras to establish some correspondences that generalize known results that hold in the group algebra case

actions of divided power hopf algebras abstract we study prime ideals in enveloping algebra smash products and use a duality construction to obtain results on prime ideals in rings on which divided power hopf algebras act these actions correspond to higher derivations first we consider chains of prime ideals in an enveloping algebra smash product over an arbitrary ring where the lie algebra is assumed to be finite dimensional abelian over a field of positive characteristic we give a bound on the length of such a chain where the ideals all have the same intersection with the coefficient ring then using an explicit construction of a duality theorem of blattner and montgomery in this context we are able to apply results on enveloping algebra smash products to study the invariant ideals of prime ideals in a ring under a locally nilpotent divided power hopf algebra action

duality theorems for rings with actions or coactions graded for s a ring on which g acts as a group of automorphisms let a be s g the skew group ring then from our morita context we obtain g s g z mg s fi where mg is the ring of matrices over s with rows and columns indexed by g and with only finitely many nonzero entries note that if s is a field then mg s sn is dense in end s g with the finite discrete topology s j to obtain our second duality theorem namely that for

semisimple strongly graded rings is semisimple meaning in this paper semisimple artinian has been studied byseveral authors the most classical result is maschke s theorem for group rings for crossed products over elds there is a satisfactory answer given by aljadeffand robinson 3 another partial answer for skew group rings was given byalfaro et al 1 a reduction of the problem to crossed products over divisionrings was rst given by jespers and okninski 10 and a more constructiveversion was given by haefner and del rio 8 so in order to give a complete answer tothe problem there is still a gap between crossed products over division rings andcrossed products over elds the rst aim of the paper is to ll this gap showingthat the semisimplicity question for crossed products over division rings reducesto the same question for crossed products over elds in theorem 3 2 we makethis reductionand then in theorem3 3 we put togetherall the piecesof the puzzle a strongly

a non linear inverse vibration problem of estimating the external forces for a system with displacement dependent parameters the conjugate gradient method i e the iterative regularization method is used in an inverse non linear force vibration problem of estimating the unknown time dependent external forces in a damped system with the displacement dependent spring constant and damping coefficients the accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements since the system parameters are functions of displacement the present study from a purely mathematical viewpoint is thus a genuine non linear inverse vibration problem the numerical simulations are performed to test the validity of the present algorithm by using different types of system parameters external forces and measurement errors results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses with a couple of second s cpu time at pentium iii 500 mhz pc

a schneider type theorem for hopf algebroids abstract comodule algebras of a hopf algebroid h with a bijective antipode i e algebra extensions b a by h are studied assuming that a lifted canonical map is a split epimorphism of modules of the non commutative base algebra of h relative injectivity of the h comodule algebra a is related to the galois property of the extension b a and also to the equivalence of the category of relative hopf modules to the category of b modules this extends a classical theorem by h j schneider on galois extensions by a hopf algebra our main tool is an observation that relative injectivity of a comodule algebra is equivalent to relative separability of a forgetful functor a notion introduced and analysed hereby

exact solution of poisson s equation with an elliptical boundary abstract an exact green s function of the 2d poisson equation for an elliptical boundary is derived in terms of elementary functions which can be readily implemented and efficiently evaluated in addition the corresponding closed form solution is derived and used for studying the convergence the accuracy and the numerical stability of both expressions the green s function for the elliptic hole is also considered by using the joukowsky mapping in a modified form in addition the green s functions of the 2d poisson equation in the rectangular domain are presented in elementary functions

graded semisimple algebras are symmetric abstract we study graded symmetric algebras which are the symmetric monoids in the monoidal category of vector spaces graded by a group we show that a finite dimensional graded semisimple algebra is graded symmetric the center of a symmetric algebra is not necessarily symmetric but we prove that the center of a finite dimensional graded division algebra is symmetric provided that the order of the grading group is not divisible by the characteristic of the base field

co frobenius hopf algebras integrals doi koppinen modules and injective objects abstract we investigate hopf algebras with non zero integral from a coalgebraic point of view categories of doi koppinen modules are studied in the special case where the defining coalgebra is left and right semiperfect and several pairs of adjoint functors are constructed as applications we give a very short proof for the uniqueness of the integrals and provide information about injective objects in the category of doi koppinen modules

covers of modules over a fixed ring abstract in this note we find conditions under which it is possible to prove the existence of relative injective covers of any module over the fixed ring r g by means of relative injective covers of modules over the base ring r the same problem is treated for flat covers

frobenius and separable functors for the category of entwined modules over cowreaths ii applications abstract let h be a quasi hopf algebra we apply results obtained in 8 to give necessary and sufficient conditions for the forgetful functor from doi hopf modules two sided hopf modules or yetter drinfeld modules over h to representations of the underlying algebra to be frobenius resp separable we show that in some situations these conditions reduce to the unimodularity and or co semisimplicity of the quasi hopf algebra h

epsilon strongly graded rings separability and semisimplicity abstract we introduce the class of epsilon strongly graded rings and show that it properly contains both the class of strongly graded rings and the class of unital partial crossed products we determine precisely when an epsilon strongly graded ring is separable over its principal component thereby we simultaneously generalize a result for strongly group graded rings by n st sescu van den bergh and van oystaeyen and a result for unital partial crossed products by bagio lazzarin and paques we also show that the class of unital partial crossed products appears in the class of epsilon strongly graded rings in a fashion similar to how the classical crossed products present themselves in the class of strongly graded rings thereby we obtain in the special case of unital partial crossed products a short proof of a general result by dokuchaev exel and simon concerning when graded rings can be presented as partial crossed products we also provide some interesting classes of examples of separable epsilon strongly graded rings with finite as well as infinite grading groups in particular we obtain an answer to a question raised by le bruyn van den bergh and van oystaeyen in 1988

clifford theory for association schemes abstract clifford theory of finite groups is generalized to association schemes it shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme the restriction of an irreducible character of a scheme to a strongly normal closed subset contains conjugate characters with same multiplicities moreover some strong relations are obtained

infinite crossed products and group graded rings in this paper we precisely determine when a crossed product r g is semiprime or prime indeed we show that these conditions ultimately depend upon the analogous conditions for the crossed products r n of the finite subgroups n of g and upon the interrelationship between the normalizers of these subgroups and the ideal structure of r the proof offered here is combinatorial in nature using the a methods and is entirely self contained furthermore since the argument applies equally well to strongly g graded rings we have opted to work in this more general context let g be a multiplicative group and let r be a ring with 1 then a crossed product r g of g over r is an associative ring determined by g r and certain other parameters to be more precise for each x e g there exists an element je r g and every element a e r g is uniquely writable as a finite sum

the closed form solution for the 2d poisson equation with a rectangular boundary the 2d green s function for the poisson equation with a rectangular boundary is investigated using the schwarz christoffel transformation method a closed form of the green s function containing jacobi elliptic functions is developed

separable functors for the category of doi hopf modules applications abstract we prove a maschke type theorem for the category of doi hopf modules in fact we give necessary and sufficient conditions for the functor that forgets the c coaction to be separable this leads to a generalized notion of integrals our results can be applied to obtain maschke type theorems for yetter drinfel d modules long dimodules and modules graded by g sets existing maschke type theorems due to doi and the authors are recovered as special cases

separability and triangulated categories abstract we prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one this applies in particular to etale algebras more generally we do this for exact separable monads

monads and comonads on module categories let a be a ring and ma the category of right a modules it is well known in module theory that any a bimodule b is an a ring if and only if the functor ab ma ma is a monad or triple similarly an a bimodule c is an a coring provided the functor ac ma ma is a comonad or cotriple the related categories of modules or algebras of ab and comodules or coalgebras of ac are well studied in the literature on the other hand the right adjoint endofunctors homa b and homa c are a comonad and a monad respectively but the corresponding co module categories did not find much attention so far the category of homa b comodules is isomorphic to the category of b modules while the category of homa c modules called c contramodules by eilenberg and moore need not be equivalent to the category of c comodules the purpose of this paper is to investigate these categories and their relationships based on some observations of the categorical background this leads to a deeper understanding and characterisations of algebraic structures such as corings bialgebras and hopf algebras for example it turns out that the categories of c comodules and homa c modules are equivalent provided c is a coseparable coring furthermore we describe equivalences between categories of homa c modules and comodules over a coring d in terms of new galois properties of bicomodules finally we characterise hopf algebras h over a commutative ring r by properties of the functor homr h and the category of mixed homr h bimodules this generalises in particular the fact that a finite dimensional vector space h is a hopf algebra if and only if the dual space h is a hopf algebra

a generalization of gabriel s galois covering functors and derived equivalences abstract let g be a group acting on a category c we give a definition for a functor f c c to be a g covering and three constructions of the orbit category c g which generalizes the notion of a galois covering of locally finite dimensional categories with group g whose action on c is free and locally bonded defined by gabriel here c g is defined for any category c and we do not require that the action of g is free or locally bounded we show that a g covering is a universal g invariant functor and is essentially given by the canonical functor c c g by using this we improve a covering technique for derived equivalences also we prove theorems describing the relationships between smash product construction and the orbit category construction by cibils and marcos 2006 without the assumption that the g action is free the orbit category construction by a cyclic group generated by an auto equivalence modulo natural isomorphisms e g the construction of cluster categories is justified by a notion of the colimit orbit category in addition we give a presentation of the orbit category of a category with a monoid action by a quiver with relations which enables us to calculate many examples

on the differential graded eilenberg moore construction abstract the eilenberg moore construction for modules over a differential graded monad is used to study a question of balmer regarding existence of an exact adjoint pair representing an exact monad a bousfield like localization for differential graded categories is realized as a special case of this construction using drinfeld quotients as applications we study some example coming from g equivariant triangulated categories and twisted derived categories

a symmetric inverse vibration problem with overdamped modes abstract several previously published results have addressed the inverse eigenvalue problem for lumped parameter non conservative systems these inverse results give conditions which allow the construction of mass normalized velocity and position coefficient matrices based on given eigenvalues and eigenvectors previous theories have examined the construction of symmetric coefficients given complex and zero eigenvalues rigid bodies here the theory of real symmetric inverse eigenvalue problems is extended to include the possibility of specifying real eigenvalues corresponding to overdamped modes specifically conditions are given that allow the construction of real symmetric mass normalized damping and stiffness matrices given specified eigenvalues and eigenvectors some of which may correspond to overdamped modes

modules graded byg sets duality and finiteness conditions an efficient technique to uncover the relationship between the representations of a group g and the representations of a subgroup h is to consider gradings by grh the class of the left h cosets of g this l w x method of study was initiated by dade in 3 where he describes the structure of the simple objects in the category r gr of g graded r modules for a g graded ring r as a generalization of the classical clifford theory a systematic investigation of modules graded by g sets was started w x w x by nastasescu et al in 9 and then continued in other papers 1 8 5 categorical properties of the category g a r gr of a graded left r modules where r is a g graded ring and a a left g set were studied first and later a series of finiteness conditions for the objects of this category were considered one natural question to ask in this framework is the following if m is an object of g a r gr where a is a finite g set and if n is an r submodule of m then which finiteness conditions i e ascending chain condition descending chain condition existence of krull dimension on n

separation of variables solutions of nonlinear reaction diffusion systems sign invariance plays an important role in the study of an explicit solution to single partial differential equations in this paper we extend the sign invariant theory to study the nonlinear reaction diffusion system as a consequence we obtain some new explicit solutions to the resulting systems and we illustrate the exact solutions for a nonlinear parabolic system

a duality theorem for vertex operator algebras abstract in this paper we prove that v h h m n v as s local vertex operator algebras where v is a simple vertex operator algebra and h is the group algebra of a finite subgroup of aut v and n dim h

clifford theory and galois theory i abstract we combine galois theory with crossed products by letting grading groups act on ground fields we show that clifford theory for suitable normal subgroups preserves such actions

graded equivalence theory with applications we develop the foundations for graded equivalence theory and apply them to investigate properties such as primeness finite representation type and vertex theory of graded rings the key fact that we prove is that for any two g graded rings r and s such that there is a category equivalence from gr r to gr s that commutes with suspensions then for any subgroup h of g the categories gr h g r and gr h g s of modules graded by the g set of right cosets are also equivalent

an inverse method for the estimation of input forces acting on non linear structural systems this study proposes an inverse method to identify input forces of non linear structural systems the method is an extension of the previous work that is limited to linear structural systems the present estimation method is composed of the extended kalman filter and a recursive least squares estimator by using the inverse method input forces acting on non linear structural systems can be estimated from measured dynamic responses in this work numerical simulations of input forces estimation of non linear lumped mass systems are performed to verify the practicality and accuracy of the proposed algorithm the simulation results demonstrate that the application of the input force estimation method to non linear structural systems is successful

covers and envelopes over gr gorenstein rings abstract in this paper we study the existence of gorenstein injective envelopes and gorenstein projective and flat covers in the category of graded modules and we relate them with the corresponding envelopes and covers in the category of modules

clifford theory of simple modules clifford theory primarily is concerned with the representations of normal subgroups and quotient groups of finite groups the basic contribution being due to a h clifford 3 modern developments founded on the concepts of group graded rings and crossed products have shown close relations with commutative and non commutative galois theory this is most conspicuous in stable clifford theory of simple modules suppose n w h g is an extension of finite groups and v is a simple f n module where f is any field since passage from the inertia group to the whole group usually is easy to handle we may and do assume that v is g invariant or h invariant stable then the annihilator i ann v of v generates a homogeneous ideal z of f h and a f h z is a fully g graded algebra with simple l component r f n z general clifford theory is concerned with such g graded algebras a and their modules cf dade 7 lo assume the l component r a is simple artinian as above then the centre k z r has in a natural way the structure of a g field the main object of study is the endomorphism ring e end v of the a module induced from the simple r module v this is a fully g graded algebra as well generalizing wedderburn s theorem we show that a z m e as g graded algebras where d is the dimension of v over the division algebra d end v theorem 2 1 in particular k z d has the same g structure with respect to e and a and e are morita equivalent in some strong sense now assume that dim r d2m2 is finite and that the schur index m m v is relatively prime to the order of the automorphism group g c k of k induced by g then the graded structure of a e can be described by some distinguished cohomology class w v e h g k more precisely w oa v determines a crossed product sz of k with g