a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part ii applications to solid mechanics problems in part i of this paper we have established the g space theory and fundamentals for w 2 formulation part ii focuses on the applications of the g space theory to formulate w 2 models for solid mechanics problems we first define a bilinear form prove some of the important properties and prove that the w 2 formulation will be spatially stable and convergent to exact solutions we then present examples of some of the possible w 2 models including the sfem ns fem es fem ns pim es pim and cs pim we show the major properties of these models 1 they are variationally consistent in a conventional sense if the solution is sought in a proper h space compatible cases 2 they pass the standard patch test when the solution is sought in a proper g space with discontinuous functions incompatible cases 3 the stiffness of the discretized model is reduced compared with the finite element method fem model and possibly to the exact model allowing us to obtain upper bound solutions with respect to both the fem and the exact solutions and 4 the w 2 models are less sensitive to the quality of the mesh and triangular meshes can be used without any accuracy problems these properties and theories have been confirmed numerically via examples solved using a number of w 2 models including compatible and incompatible cases we shall see that the g space theory and the w 2 forms can formulate a variety of stable and convergent numerical methods with the fem as one special case

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

free in plane vibration analysis of rectangular plates with elastic support normal to the boundaries the superposition method is employed to analyze the effects of elastic edge support on the in plane free vibration frequencies and mode shapes of rectangular plates the elastic edge support is considered to be uniformly distributed along the plate edges and symmetrically distributed with respect to the plate central axes in addition exact solutions are also obtained for a family of simply supported plates whose eigenvalues constitute upper limits for those of the elastically supported plates an array of highly accurate eigenvalues for the completely free plate is also computed in order to provide lower limit eigenvalues eigenvalues are computed and tabulated for elastically supported plates of various aspect ratios and dimensionless elastic support coefficients

a novel alpha finite element method αfem for exact solution to mechanics problems using triangular and tetrahedral elements abstract the paper presents an alpha finite element method fem for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains three node triangular fem t3 and four node tetrahedral fem t4 elements with a scale factor are formulated for two dimensional 2d and three dimensional 3d problems respectively the essential idea of the method is the use of a scale factor 0 1 to obtain a combined model of the standard fully compatible model of the fem and a quasi equilibrium model of the node based smoothed fem n sfem this novel combination of the fem and n sfem makes the best use of the upper bound property of the n sfem and the lower bound property of the standard fem using meshes with the same aspect ratio a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems the proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation numerical results for 2d using fem t3 and 3d using fem t4 problems confirm that the present method gives the much more accurate solution comparing to both the standard fem and the n sfem with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems

homomorphisms between algebras of lipschitz functions with the values in function algebras abstract we give a characterization of algebra homomorphisms and isomorphisms between banach algebras of lipschitz functions with the values in unital commutative c algebras we prove that such homomorphisms are composition operators of the form and preserve some properties

local automorphisms of nest subalgebras of factor von neumann algebras in this paper it is proved that every surjective weakly continuous linear local automorphism of nest subalgebras with non trivial nests of factor von neumann algebras is an automorphism and that every surjective linear 2 local automorphism of nest algebras with non trivial nests of factor von neumann algebras is an automorphism

rotation based rls algorithms unified derivations numerical properties and parallel implementations this work presents a unified derivation of four rotation based recursive least squares rls algorithms they solve the adaptive least squares problems of the linear combiner the linear combiner without a desired signal the single channel and the multichannel linear prediction and transversal filtering compared to other approaches the authors derivation is simpler and unified and may be useful to readers for better understanding the algorithms and their relationships moreover it enables improvements of some algorithms in the literature in both the computational and the numerical issues all algorithms derived in this work are based on givens rotations they offer superior numerical properties as shown by computer simulations they are computationally efficient and highly concurrent aspects of parallel implementation and parameter identification are discussed

local derivations of nest subalgebras of von neumann algebras in this paper it is proved that every norm continuous linear local derivation of a nest subalgebra of a factor von neumann algebra is a derivation and that every linear 2 local derivation of a nest subalgebra of a factor von neumann algebra is a derivation

local derivations on certain csl algebras in this paper it is shown that every norm continuous linear local derivation from an arbitrary csl algebra whose lattice is generated by finitely many independent nests into any ultraweakly closed subalgebra which contains the algebra is an inner derivation and that every norm continuous linear local derivation from an arbitrary csl algebra whose lattice is completely distributive into any ultraweakly closed subalgebra which contains the algebra is a derivation

bounds on natural frequencies of composite circular plates integral equation methods abstract the problem of finding upper and lower bounds to the natural frequencies of free vibration of a circular plate with stepped radial density has been investigated such problems involving discontinuous coefficients in the governing differential equation are formulated with an integral equation by using a green function and the basic theory of linear integral equations it is shown that eigenvalue estimation techniques based on the integral equation formulation are more effective than those based on the traditional differential equation formulation by using the galerkin method the integral equation formulation is shown to provide more accurate upper bounds than the differential equation formulation for both the clamped and simply supported plates additionally it is shown that the corresponding green functions can be used to supply improvable lower bounds

local derivations on operator algebras abstract when attempting to find sufficient conditions for a linear mapping to be a derivation an obvious candidate is the concept of a local derivation local derivations on operator algebras have been investigated in recent papers of kadison j algebra130 1990 494 509 and larson and sourour proc symp pure math 51 1990 187 194 a local derivation is a norm continuous linear map from an operator algebra a into an a bimodule m which agrees with some derivation at each point in the algebra we show that if a is the direct limit of finite dimensional csl algebras via extendable embeddings e g a triangular af algebra then a local derivation on a must be a derivation further we show that for many finite dimensional operator algebras any inner local derivation must be an inner derivation

on the time response of square plates on unilateral support abstract transient response and vibrations of an elastic thin plate supported on a unilateral foundation are presented the displacement function of the plate is approximated by using the eigenfunctions of the completely free beam in the application of the galerkin method the boundary conditions which cannot be satisfied by the beam functions at the corners of the plate and the edges are compensated by suitable additions to the governing equation although the procedure can readily be used to solve problems of plates under the action of any arbitrary loads the problem solved numerically involves a single concentrated force numerical results are presented in figures to clarify the dynamic behaviour of the plate

transient vibration analysis of a completely free plate using modes obtained by gorman s superposition method abstract this paper shows that the transient response of a plate undergoing flexural vibration can be calculated accurately and efficiently using the natural frequencies and modes obtained from the superposition method the response of a completely free plate is used to demonstrate this the case considered is one where all supports of a simply supported thin rectangular plate under self weight are suddenly removed the resulting motion consists of a combination of the natural modes of a completely free plate the modal superposition method is used for determining the transient response and the natural frequencies and mode shapes of the plates used are obtained by gorman s superposition method these are compared with corresponding results based on the modes using the rayleigh ritz method using the ordinary and degenerated free free beam functions there is an excellent agreement between the results from both approaches but the superposition method has shown faster convergence and the results may serve as benchmarks for the transient response of completely free plates

non linear transient analysis of moderately thick laminated composite plates the non linear transient analysis of the shear deformable laminated composite plates subjected to step ramp and sinusoidal loading is presented the clamped simply supported free and their combinations non levy type of boundary conditions are considered the formulation is based on the mindlin first order shear deformation theory and von karman non linearity the methodology of the solution is based on the chebyshev series technique houbolt time marching scheme and quadratic extrapolation technique are used for the temporal discretization and linearization respectively the effects of magnitude and duration of loading rotary inertia in plane inertia b a a h lamination scheme and boundary conditions on the central displacement response are studied typical results are presented in dimensionless graphical forms for different parameters and loading conditions

free vibration analysis of completely free rectangular plates by the superposition galerkin method the superposition galerkin method for analyzing the free vibration of thin isotropic and orthotropic plates as well as transverse shear deformable plates was introduced in recent years it has an advantage over the traditional superposition method in that it gives equally accurate results but requires much less work on the part of the analyst unfortunately it has not been possible up to this time to apply it to plates with free edge conditions this was due to mixed derivatives appearing in the formulation of free edge boundary conditions in this paper it is shown how with the superposition of specially selected sets of forced vibration solutions building blocks the above limitations are avoided while the technique is applied here to the analysis of fully symmetric modes only it is demonstrated how the superposition galerkin method can be applied to any of the above plate problems regardless of the combination of free edge boundary conditions to be imposed

on superaccurate finite elements and their duals for eigenvalue computation in eigenvalue problems of elastic media in free vibration a discrete model is usually derived by using the finite element method and the accuracy of the elements is of concern in practical applications the present note reviews the accuracy of certain classes of finite element models in two point boundary eigenvalue problems and points to some special elements that exist within these classes

characterizing derivations for any nest algebras on banach spaces by their behaviors at an injective operator abstract let n be a nest on a complex banach space x and let alg n be the associated nest algebra we say that an operator z alg n is an all derivable point of alg n if every linear map from alg n into itself derivable at z i e satisfies a b a b z for any a b alg n with a b z is a derivation in this paper it is shown that every injective operator and every operator with dense range in alg n are all derivable points of alg n without any additional assumption on the nest

theoretical aspects of the smoothed finite element method sfem this paper examines the theoretical bases for the smoothed finite element method sfem which was formulated by incorporating cell wise strain smoothing operation into standard compatible finite element method fem the weak form of sfem can be derived from the hu washizu three field variational principle for elastic problems it is proved that 1d linear element and 2d linear triangle element in sfem are identical to their counterparts in fem while 2d bilinear quadrilateral elements in sfem are different from that of fem when the number of smoothing cells scs of the elements equals 1 the sfem solution is proved to be variationally consistent and has the same properties with those of fem using reduced integration when sc approaches infinity the sfem solution will approach the solution of the standard displacement compatible fem model when sc is a finite number larger than 1 the sfem solutions are not variationally consistent but energy consistent and will change monotonously from the solution of sfem sc 1 to that of sfem sc it is suggested that there exists an optimal number of sc such that the sfem solution is closest to the exact solution the properties of sfem are confirmed by numerical examples copyright 2006 john wiley sons ltd

local 2 cocycles of nest subalgebras of factor von neumann algebras in this paper it is proved that every weakly continuous local 2 cocycle of a nest subalgebra of a factor von neumann algebra with coefficients in the factor von neumann algebra is a 2 cocycle

bounded natural frequencies of completely free rectangular plates this paper presents dimensionless natural frequency parameters for completely free rectangular plates calculated using the superposition method sm and the finite difference method fdm the convergence tests show that while the sm gives upper bound results the fdm gives lower bound results the results obtained using the fdm appears to be the best lower bound results available to date together with the upper bound results from the sm the maximum possible error in the first 12 non zero natural frequency parameters for completely free rectangular plates of various aspects ratios ranging from 1 1 to 3 1 can be determined from the results presented here

on the duality between the fast transversal and the fast qrd adaptive least squares algorithms the duality between the fast transversal and the fast qrd adaptive least squares algorithms is established it is shown that these two algorithmic families are related via a time varying state transformation the state transformation method is then applied to both the fast kalman as well as the faest ptf algorithm to derive fast qrd counterparts

the superposition galerkin method for free vibration analysis of rectangular plates abstract it is known that exploitation of the traditional superposition method for analyzing plate free vibration problems becomes a very demanding and difficult task when one moves from thin isotropic plate theory to be the thick plate mindlin theory and to the analysis of laminated plates difficulties arise because of the vast families of roots encountered real and complex when solving associated differential equations the presence of hyperbolic functions tends to produce computer over flow and under flow and computational difficulties in this paper the modified superposition galerkin method is introduced all of the above problems are eliminated and excellent agreement is encountered when results obtained by both methods are compared

free vibration analysis by the superposition method of rectangular mindlin plates with internal columns resting on uniform elastic edge supports free vibration analysis of rectangular mindlin plates is carried out via the superposition method and is shown to produce accurate results the analytical method proposed by the authors in this paper solves the problem for the case where the plate has simultaneous elastic edge and internal supports the conditions of edge supports are uniform lateral rotational and torsional elastic supports whereas the internal supports are column supports with finite area compatibility between the plate and column is achieved by requiring that the column and plate rotations be equal the results presented herein are verified through comparison with results presented by others numerical examples presented in this study confirm that the analytical method is able to model the property of the elastic edge supports while simultaneously considering the effect of column restraint an effect which increases with column number and area

derivable mappings at unit operator on nest algebras abstract let a be an operator subalgebra with the unit operator i in b h we say that a linear mapping from a into itself is a derivable mapping at i if st s t s t for any s t a with st i in this paper we show the following main result every strongly operator topology continuous derivable mapping at i on a nest algebra alg n is an inner derivation

annihilator preserving maps multipliers and derivations abstract for a commutative subspace lattice l in a von neumann algebra n and a bounded linear map f n alg l b h we show that if af b c 0 for all a b c n alg l satisfying ab bc 0 then f is a generalized derivation for a unital c algebra a a unital banach a bimodule m and a bounded linear map f a m we prove that if f a b 0 for all a b a with ab 0 then f is a left multiplier as a consequence every bounded local derivation from a c algebra to a banach a bimodule is a derivation we also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier

generalized derivable mappings at zero point on some reflexive operator algebras abstract let a be a subalgebra with the unit operator i in b h we say that a linear mapping from a into b h is a generalized derivable mapping at zero point if st s t s t s i t for any s t a with st 0 in this paper we show the following main result every norm continuous generalized derivable mapping at zero point on finite csl algebras is a generalized derivation

local isometries on spaces of continuous functions let x and y be banach spaces and s a subset of the space of linear continuous operators from x to y we say that an operator t belongs locally to s if for every x x there is s s possibly depending on x such that tx sx pointwise should be better than locally but we have followed tradition if each operator that belongs locally to s belongs in fact to s we say that s is algebraically reflexive when y x and s iso x is the group of isometries of x we say that t is a local isometry of x in this paper isometry means linear surjective isometry similarly a local automorphism of a banach algebra is an operator which agrees at every point with some automorphism also we will consider approximate local isometries and automorphisms these are operators having with the following property given x x and e 0 there is an isometry respectively an automorphism s of x such that tx sx e the study of local isometries and automorphisms of banach algebras spurred a considerable interest in recent years see the bibliography of the dissertation 16 in this paper we deal with local isometries and automorphisms of the algebras c0 l as usual we write c0 l or c k 0 l for the banach algebra of all continuous k valued functions on the locally compact space l vanishing at infinity where k is either c or r if l is compact the subscript will be omitted by the banach stone theorem if t is local isometry of c0 l then for each f there are a homeomorphism of l and a continuous unitary u l k such that tf u f

an edge based smoothed finite element method es fem for static free and forced vibration analyses of solids abstract this paper presents an edge based smoothed finite element method es fem to significantly improve the accuracy of the finite element method fem without much changing to the standard fem settings the es fem can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains in the es fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles intensive numerical results demonstrated that the es fem possesses the following excellent properties 1 the es fem model possesses a close to exact stiffness it is much softer than the overly stiff fem and much stiffer than the overly soft ns fem model 2 the results are often found superconvergence and ultra accurate much more accurate than the linear triangular elements of fem and even more accurate than those of the fem using quadrilateral elements with the same sets of nodes 3 there are no spurious non zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and 4 the implementation of the method is straightforward and no penalty parameter is used and the computational efficiency is better than the fem using the same sets of nodes in addition a novel domain based selective scheme is proposed leading to a combined es ns fem model that is immune from volumetric locking and hence works very well for nearly incompressible materials these properties of the es fem are confirmed using examples of static free and forced vibration analyses of solids

a rayleigh ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions abstract to overcome the lack of a more general method for free vibration analysis of trapezoidal plates a computationally efficient and highly accurate rayleigh ritz approach with the newly developed orthogonal plate functions is proposed to solve these problems with any combination of clamped simply supported and free edge support conditions the deflection of the plate is approximated by a set of two dimensional orthogonal plate functions generated using the gram schmidt procedure which expresses the entire plate domain into two implicitly related variables in the present paper the effects of the fibre orientation on the vibrational behaviour of the plates are considered the numerical results for isotropic and anisotropic trapezoidal plates are presented where possible the numerical results are verified with other existing values in the literature

characterizations of derivations on triangular rings additive maps derivable at idempotents abstract let t be a triangular ring an element z t is said to be a full derivable point of t if every additive map from t into itself derivable at z i e a b a b z for every a b t with ab z is in fact a derivation in this paper under some mild conditions on triangular ring t we show that some idempotent elements of t are full derivable points as an application we get that for any nontrivial nest n in a factor von neumann algebra r every nonzero idempotent element q satisfying pq q qp p for some projection p n is a full derivable point of the nest subalgebra alg n of r

on the duality between fast qr methods and lattice methods in least squares adaptive filtering the authors show that fast qr methods and lattice methods in least squares adaptive filtering are duals and follow from identical geometric principles whereas the lattice methods compute the residuals of a projection operation via the forward and backward prediction errors the qr methods compute instead the weights used in the projections within this framework the parameter identification problem is solved using fast qr methods by showing that the reflection coefficients and tap parameters of a least squares lattice filter operating in the joint process mode are immediately available as internal variables in the fast qr algorithms this parameter set can be readily exploited in system identification signal analysis and linear predictive coding for example the relations derived also lead to a fast least squares algorithm of minimal complexity that is a hybrid between a qr and a lattice algorithm the algorithm combines the order recursive properties of the lattice approach with the robust numerical behavior of the qr approach

accurate in plane free vibration analysis of rectangular orthotropic plates accurate analytical type solutions are obtained for the free in plane vibration eigenvalues and mode shapes of fully clamped orthotropic rectangular plates appropriate governing differential equations for orthotropic plates are developed in dimensionless form and employed solutions are obtained by the method of superposition it will be apparent that the solution procedure can be readily extended to analyze plates with other types of classical boundary conditions the work reported is a natural extension of earlier work related to the in plane vibration of isotropic plates this appears to be the first analytical type study related to orthotropic plate in plane vibration it is expected that results tabulated here will form a valuable reference against which the results of other researchers may be compared

accurate and elegant free vibration and buckling studies of orthotropic rectangular plates using untruncated infinite series this paper presents the extension of a novel superposition method put forth for static analysis earlier for carrying out free vibration and bifurcation buckling studies of orthotropic rectangular plates with any combination of classical boundary conditions viz clamped simply supported and free edges it is shown that use of infinite series counterparts of conventional levy type closed form expressions result in a tremendous simplification of the problem without any compromise on accuracy the complicating effects of an elastic foundation and initial stresses are also shown to be easily accounted for results useful as benchmarks in future are presented for a chosen set of cases

the free flexural vibration of right triangular isotropic and orthotropic plates abstract a simple straighforward rayleigh ritz analysis is given for the determination of an eigenproblem for the free flexural vibration of thin right triangular plates having any combination of the classical free simply supported or clamped boundary conditions simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals the analysis is developed for specially orthotropic plates but numerical results are given primarily for the isotropic case

on the accurate analysis of free vibration of open circular cylindrical shells abstract this paper considers the analytical methods used and the boundary conditions encountered in the accurate free vibration analysis of open circular cylindrical shells the simple boundary conditions associated with the donnell mushtari theory of thin shells are classified into primary and secondary boundary conditions different combinations of these primary and secondary boundary conditions lead to the use of different analytical methods exact solutions for basic shells with different combinations of primary boundary conditions are obtained using the generalized navier method accurate solutions for shells with secondary and mixed boundary conditions are obtained by using the method of superposition one needs to investigate only four primary and nine secondary basic shells in order to obtain solutions for shells with arbitrary combinations of simple boundary conditions

an efficient differential quadrature methodology for free vibration analysis of arbitrary straight sided quadrilateral thin plates in this paper a new differential quadrature dq methodology is employed to study free vibration of irregular quadrilateral straight sided thin plates a four nodded super element is used to map the irregular physical domain into a square domain in the computational domain second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains the only degree of freedom within the domain is the displacement whereas along the boundaries the displacement as well as the second order derivative of the displacement with respect to associated normal co ordinate variable in computational domain are the two degrees of freedom implementing the method the formulation for the dq method for the free vibration analysis of plates of straight sided shapes was presented together with the implementation procedure for the different boundary conditions to demonstrate the accuracy convergency and stability of the new methodology detail studies are made on isotropic plates at acute angles with different geometries boundary and loading conditions including dq free edge boundary condition implementations accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved

on derivable mappings abstract a linear mapping from an algebra a into an a bimodule m is called derivable at c a if a b a b c for all a b a with a b c for a norm closed unital subalgebra a of operators on a banach space x we show that if c a has a right inverse in b x and the linear span of the range of rank one operators in a is dense in x then the only derivable mappings at c from a into b x are derivations in particular the result holds for all completely distributive subspace lattice algebras j subspace lattice algebras and norm closed unital standard algebras of b x as an application every jordan derivation from such an algebra into b x is a derivation for a large class of reflexive algebras a on a banach space x we show that inner derivations from a into b x can be characterized by boundedness and derivability at any fixed c a provided c has a right inverse in b x we also show that if a is a canonical subalgebra of an af c algebra b and m is a unital banach a bimodule then every bounded local derivation from a into m is a derivation moreover every bounded linear mapping from a into b that is derivable at the unit i is a derivation

accurate analytical type solutions for the free in plane vibration of clamped and simply supported rectangular plates highly accurate analytical type solutions are obtained by means of the superposition method for the free in plane vibration frequencies and mode shapes of fully clamped rectangular plates the modes are separated into three distinct families and each family is handled separately excellent agreement is encountered when computed results are compared with results obtained by other methods following the obtaining of solutions for the fully clamped plate it is shown how this work can be exploited to obtain exact levy type solutions for the free in plane vibration modes of the plate with simple support along all edges the pure shear and extensional vibration modes characteristic of the latter plate problem are handled separately again excellent agreement with results obtained by other means is encountered a limited number of mode shapes for the fully clamped plate are presented

a linearly conforming point interpolation method lc pim for three dimensional elasticity problems linearly conforming point interpolation method lc pim is formulated for three dimensional elasticity problems in this method shape functions are generated using point interpolation method by adopting polynomial basis functions and local supporting nodes are selected based on the background cells the shape functions so constructed have the kronecker delta functions property and it allows straightforward imposition of point essential boundary conditions galerkin weak form is used for creating discretized system equations and a nodal integration scheme with strain smoothing operation is used to perform the numerical integration the present lc pim can guarantee linear exactness and monotonic convergence for the numerical results numerical examples are used to examine the present method in terms of accuracy convergence and efficiency compared with the finite element method using linear elements the lc pim can achieve better efficiency and higher accuracy especially for stresses copyright 2007 john wiley sons ltd

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

upper bound solution to elasticity problems a unique property of the linearly conforming point interpolation method lc pim it is well known that the displacement based fully compatible finite element method fem provides a lower bound in energy norm for the exact solution to elasticity problems it is however much more difficult to bound the solution from above for general problems in elasticity and it has been a dream of many decades to find a systematical way to obtain such an upper bound this paper presents a very important and unique property of the linearly conforming point interpolation method lc pim it provides a general means to obtain an upper bound solution in energy norm for elasticity problems this paper conducts first a thorough theoretical study on the lc pim we derive its weak form based on variational principles study a number of properties of the lc pim and prove that lc pim is variationally consistent and that it produces upper bound solutions we then demonstrate these properties through intensive numerical studies with many examples of 1d 2d and 3d problems using the lc pim together with the fem we now have a systematical way to numerically obtain both upper and lower bounds of the exact solution to elasticity problems as shown in these example problems copyright 2007 john wiley sons ltd

on the smoothed finite element method recently liu et al proposed the smoothed finite element method by using the non mapped shape functions and then introducing the strain smoothing operator when evaluating the element stiffness in the framework of the finite element method however the theories and examples by liu et al are not sufficient for general quadrilateral elements this paper shows that the non mapped shape functions used in the smoothed finite element have disadvantages in existence linearity non negativity and patch test copyright 2008 john wiley sons ltd

the free flexural vibration of isotropic and orthotropic general triangular shaped plates abstract the rayleigh ritz method is used with simple polynomials as admissible functions to obtain an eigenvalue equation for the free flexural vibration of thin isotropic and specially orthotropic general triangular plates the plates may have any combination of the classical free simply supported or clamped boundary conditions the convergence and accuracy of the solution is illustrated and numerical results are presented for a variety of isotropic plates and for orthotropic cantilever plates

bounds on natural frequencies of composite circular membranes integral equation methods this paper is concerned with finding upper and lower bounds for the natural frequencies of vibration of a circular membrane with stepped radial density such problems involving discontinuous coefficients in the differential equation may be treated by using classical variational methods however it is shown here that eigenvalue estimation techniques based on an integral equation formulation are more effective integral equation methods provide more accurate upper bounds for a comparable amount of effort and supply improvable lower bounds as well

the fast adaptive rotor s rls algorithm a fast algorithm for implementation of the qr factorization based recursive least squares rls adaptive filter is discussed this fast adaptive rotors far algorithm can be implemented with a pipelined array of processors called rotors and cisors the rotors compute 2 2 orthogonal givens rotations and the cisors compute the cosines and sines of the angles used in the rotors the algorithm requires 4n rotors and 2n cisors at each iteration to compute the solution to the rls problem the algorithm is numerically stable the far algorithm is derived using a single generic updating formula for orthogonal matrices which is introduced and derived whereas the generic updating formula is reminiscent of previous fast transversal filters and fast lattice algorithms the set of internally propogated adaptive filter quantities is entirely different and constitutes yet another complete characterization of the rls covariance and the forward backward and pinning estimation problems

2 local triple homomorphisms on von neumann algebras and jbw triples abstract we prove that every not necessarily linear nor continuous 2 local triple homomorphism from a jbw triple into a jb triple is linear and a triple homomorphism consequently every 2 local triple homomorphism from a von neumann algebra respectively from a jbw algebra into a c algebra respectively into a jb algebra is linear and a triple homomorphism

free in plane vibration analysis of rectangular plates by the method of superposition abstract the superposition method is introduced as a means for obtaining analytical type solutions for free in plane vibration of rectangular plates the governing differential equations and boundary conditions are expressed in dimensionless form the problem of free in plane vibration of the completely free rectangular plate is resolved for illustrative purposes convergence is found to be rapid and excellent agreement between computed results and those obtained by previous authors utilizing the rayleigh ritz energy method is obtained it is pointed out that following procedures analogous to those utilized in resolving lateral plate vibration problems in plane free vibration problems related to point supported plates plates with in plane elastic boundary support etc are now amenable to solution by this method

a semi analytical method for the free vibration of doubly curved shells of revolution abstract in this paper a semi analytical method is used to investigate the free vibration of doubly curved shells of revolution with arbitrary boundary conditions the doubly curved shells of revolution are divided into their segments in the meridional direction and the theoretical model for vibration analysis is formulated by applying flugge s thin shell theory regardless of the boundary conditions the displacement functions of shell segments are composed by the jacobi polynomials along the revolution axis direction and the standard fourier series along the circumferential direction the boundary conditions at the ends of the doubly curved shells of revolution and the continuous conditions at two adjacent segments were enforced by the penalty method then the natural frequencies of the doubly curved shells are obtained by using the rayleigh ritz method for arbitrary boundary conditions this method does not require any changes to the mathematical model or the displacement functions and it is very effective in the analysis of free vibration for doubly curved shells of revolution the credibility and exactness of proposed method are compared with the results of finite element method fem and some numerical results are reported for free vibration of the doubly curved shells of revolution under classical and elastic boundary conditions results of this paper can provide reference data for future studies in related field

a note on 2 local automorphisms of digraph algebras abstract in this note we show that every 2 local automorphism of a digraph algebra a is an automorphism if in addition a is symmetric moreover we produce an example to clarify that the conclusion may not be true if a has not the extra condition of symmetry by this means we give a negative answer to the question about whether every 2 local automorphism of a digraph algebra is automatically an automorphism

upper and lower bounds for natural frequencies a property of the smoothed finite element methods node based smoothed finite element method ns fem using triangular type of elements has been found capable to produce upper bound solutions to the exact solutions for force driving static solid mechanics problems due to its monotonic soft behavior this paper aims to formulate an ns fem for lower bounds of the natural frequencies for free vibration problems to make the ns fem temporally stable an fem is devised by combining the compatible and smoothed strain fields in a partition of unity fashion controlled by 0 1 so that both the properties of stiff fem and the monotonically soft ns fem models can be properly combined for a desired purpose for temporally stabilizing ns fem is chosen small so that it acts like a regularization parameter making the ns fem stable but still with sufficient softness ensuring lower bounds for natural frequency solution our numerical studies demonstrate that 1 using a proper the spurious non zero energy modes can be removed and the ns fem becomes temporally stable 2 the stabilized ns fem becomes a general approach for solids to obtain lower bounds to the exact natural frequencies over the whole spectrum 3 fem can even be tuned for obtaining nearly exact natural frequencies

free and forced flexural vibration analysis of cantilever plates with attached point mass abstract in this paper the method of superposition or the gorman method is employed to obtain an analytical solution for free and forced vibrations of cantilever plates carrying point masses the free lateral vibration analysis is carried out by employing five building blocks four for the cantilever plate and one for the point mass computed eigenvalues show that the proposed scheme is accurate and convergent for free vibration analysis once the eigen analysis is completed the modal summation method is then used to deal with the base induced lateral vibration of cantilever plates carrying a point mass effects of mass ratios and locations of the point mass on eigenvalues and modal participation factors are investigated for square and rectangular plates

upper and lower bounds for frequencies of trapezoidal and triangular plates upper and lower bounds are given for the two lowest frequencies of vibration of clamped trapezoidal and triangular plates it is believed that this is the first time that rigorous bounds have been calculated for the vibrational frequencies of plates of these shapes

reflexivity of the automorphism and isometry groups of the suspension of b h the aim of this paper is to show that the automorphism and isometry groups of the suspension of b h h being a separable infinite dimensional hilbert space are algebraically reflexive this means that every local automorphism respectively every local surjective isometry ofc0 r b h is an automorphism respectively a surjective isometry

stabilized conforming nodal integration in the natural element method a stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non sibsonian interpolation in this approach both the shape functions and the integration scheme are defined through use of first order voronoi diagrams the method illustrates improved performance and significant advantages over previous natural neighbour formulations the method also shows substantial promise for problems with large deformations and for the computation of higher order gradients copyright 2004 john wiley sons ltd

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

vibrational frequencies of clamped plates of variable thickness abstract a method is presented for computing lower and upper bounds for vibrational frequencies of clamped plates with general thickness variations the method is illustrated for plates with linear tapers

local lie derivations of nest algebras abstract let n be a nest on a hilbert space h and alg n be the associated nest algebra we prove that every local lie derivation from alg n into b h is a lie derivation

free vibration analysis of doubly curved shallow shells using the superposition galerkin method abstract this paper demonstrates the applicability of the superposition method for free vibration analysis of doubly curved thin shallow shells of rectangular planform with any possible combination of simply supported and clamped edges the same building block yields the natural frequencies for 55 combinations of edge conditions the natural frequency parameters of the shells were obtained using the superposition galerkin method sgm for seven sets of boundary conditions several different curvature ratios and two aspect ratios the sgm uses approximate steady state solutions as building blocks but the method proves to be accurate and efficient it has also been shown that even with approximate building blocks the monotonic nature of convergence of the natural frequencies with respect to the number of driving coefficients holds as long as the number of admissible functions in the steady state solution is kept constant the results for natural frequencies of the seven boundary conditions may be considered as benchmarks