sofic groups and direct finiteness abstract we construct an analogue of von neumann s affiliated algebras for sofic group algebras over arbitrary fields consequently we settle kaplansky s direct finiteness conjecture for sofic groups

unified response probability distribution analysis of two hybrid uncertain acoustic fields abstract for the response analysis of uncertain acoustic fields with limited information two hybrid uncertain models have been developed one is the hybrid probability and interval model in which the probability and interval variables exist simultaneously the other one is the hybrid interval probability model in which some distribution parameters of probability variables are expressed as interval variables for the unified response probability distribution analysis of acoustic fields under two hybrid uncertain models an inverse mapping hybrid perturbation method imhpm is proposed in imhpm the responses of two hybrid uncertain acoustic fields are converted to invertible functions of probability variables based on the taylor series expansion according to the inverse mapping relationships between responses and probability variables the formal expressions of the response probability distributions are yielded on the basis of the change of variable technique the variational ranges of the response probability distributions are estimated by the interval perturbation technique the effectiveness and efficiency of the proposed method for the unified response probability distribution analysis of two hybrid uncertain acoustic fields are investigated by a numerical example

fuzzy interval finite element statistical energy analysis for mid frequency analysis of built up systems with mixed fuzzy and interval parameters abstract this paper introduces mixed fuzzy and interval parametric uncertainties into the fe components of the hybrid finite element statistical energy analysis fe sea model for mid frequency analysis of built up systems thus an uncertain ensemble combining non parametric with mixed fuzzy and interval parametric uncertainties comes into being a fuzzy interval finite element statistical energy analysis fife sea framework is proposed to obtain the uncertain responses of built up systems which are described as intervals with fuzzy bounds termed as fuzzy bounded intervals fbis in this paper based on the level cut technique a first order fuzzy interval perturbation fe sea ffipfe sea and a second order fuzzy interval perturbation fe sea method sfipfe sea are developed to handle the mixed parametric uncertainties efficiently ffipfe sea approximates the response functions by the first order taylor series while sfipfe sea improves the accuracy by considering the second order items of taylor series in which all the mixed second order items are neglected to further improve the accuracy a chebyshev fuzzy interval method cfim is proposed in which the chebyshev polynomials is used to approximate the response functions the fbis are eventually reconstructed by assembling the extrema solutions at all cut levels numerical results on two built up systems verify the effectiveness of the proposed methods

hybrid uncertain analysis for structural acoustic problem with random and interval parameters abstract in this paper hybrid perturbation monte carlo method hpmcm and hybrid perturbation vertex method hpvm are developed for the hybrid uncertain structural acoustic problem with random and interval variables the random variables are used to treat the uncertain parameters with sufficient information whereas the interval variables are used to treat the uncertain parameters with limited information in hpmcm the intervals of expectation and variance of the frequency response vector are calculated by a combination of random interval matrix perturbation method random interval moment method and monte carlo method in hpvm a monotonicity analysis is conducted for the frequency response vector based on the random interval matrix perturbation method and then the intervals of expectation and variance of the frequency response vector are calculated by employing the random interval moment method and the vertex method numerical results on a shell structural acoustic problem verify the effectiveness and high efficiency of hpvm compared with hpmcm

topological properties of banach spaces weakly compact sets in banach spaces are fragmentable we introduce the weaker notion of the a fragmentability of a subset of a banach space a notion that has a far wider range of applicability we prove that all weakly cech analytic subsets of a banach space are a fragmented this implies that all banach spaces having kadec norms are a fragmented however l is not fragmented

a stability property for locally uniformly rotund renorming abstract it is proved that c k e the space of all continuous functions on a hausdorff compact space k taking values in a banach space e admits an equivalent locally uniformly rotund norm if c k and e do so moreover if the equivalent lur norms on c k and e are lower semicontinuous with respect to some weak topologies the lur norm on c k e can be chosen to be lower semicontinuous with respect to an appropriate weak topology as a consequence we prove that if x and y are two hausdorff compacta and c x c y admit equivalent pointwise lower semicontinuous lur norms then so does c x y

hybrid uncertain natural frequency analysis for structures with random and interval fields abstract this paper presents a robust non deterministic free vibration analysis for engineering structures involving hybrid yet spatially dependent uncertain system parameters distinguished from the conventional hybrid uncertain eigenvalue problem the concept of interval field is enclosed with random field model such that both the stochastic and non stochastic representations of the spatial dependency of the uncertainties are simultaneously incorporated within a unified non deterministic free vibration analysis in order to determine the probabilistic characteristics i e means and standard deviations of the extremities of structural natural frequencies an extended unified interval stochastic sampling x uiss method is implemented for the purpose of effective hybrid uncertain free vibration analysis by meticulously blending sharpness promised interval eigenvalue analysis with stochastic sampling techniques the stochastic profiles i e probability density functions pdfs and the cumulative distribution functions cdfs of the extreme bounds of the structural natural frequencies can be rigorously established by utilizing the adequate statistical inference methods the applicability and effectiveness of the proposed computational framework are evidently demonstrated through the numerical investigations on various practically motivated engineering structures

optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval an optimization method for uncertain structures is suggested based on convex model and a satisfaction degree of interval in the investigated problem the uncertainty only exists in constraints convex model is used to describe the uncertainty in which the intervals of the uncertain parameters are only needed not necessarily to know the precise probability distributions a satisfaction degree of interval which represents the possibility that one interval is smaller than another is employed to deal with the uncertain constraints based on a predetermined satisfaction degree level the uncertain constraints are transformed to deterministic ones and the transformed optimization problem can be solved by traditional optimization methods for complex structural problems that the optimization model cannot be expressed in an explicit form the interval analysis method is adopted to calculate the intervals of the constraints efficiently and whereby eliminate the optimization nesting two numerical examples have been presented to demonstrate the efficiency of the suggested method

stochastic basis expansions applied to acoustic propagation in an uncertain range and depth dependent multi layered waveguide we study the utility of stochastic basis expansions in acoustic propagation through a multi layered ocean waveguide in the presence of environmental uncertainty environmental uncertainty means that the parameters that describe the waveguide are treated probabilistically specifically in the differential equation governing propagation the uncertainty appears in the sound speed profile as an explicit dependence on a set of random variables this implies that the acoustic field itself is a random field stochastic basis expansions are attractive because of their often exponential convergence we use a complete set of multivariate orthogonal polynomials to compute the acoustic field s statistics the field propagates by a wide angle parabolic equation through a rectangular waveguide comprised of three layers separated by two horizontal interfaces a pressure release surface and hard bottom bound the waveguide the water s sound speed is a constant perturbed by a small random range and depth dependent ter

on the unit conjecture for supersoluble group algebras abstract we introduce structure theorems for the study of the unit conjecture for group algebras of torsion free supersoluble groups motivated by work of p m cohn we introduce the class of x y n group algebras kg and following d s passman we define an induced length function l k g n using the fact that g has the infinite dihedral group as a homomorphic image we develop splitting theorems for x y n group algebras and as an application show that if k g is a unit then l l 1 we extend our analysis of splittings to obtain a canonical reduced split form for all units in x y n group algebras this leads to the study of group algebras of virtually abelian groups and their representations as subalgebras of suitable matrix rings where we develop a determinant condition for units in such group algebras we apply our results to the fours group x y x y 2 x 1 y 2 y x 2 y 1 x 2 and show that over any field k the group algebra k has no non trivial unit of small l length using this and the fact that l is equivariant under all k automorphisms obtained k linearly from automorphisms we prove that no subset of the promislow set p is the support of a non trivial unit in k for any field k in particular this settles a long standing question and shows that the promislow set is itself not the support of a unit in k we then give an introduction to the theory of consistent chains toward a preliminary analysis of units of higher l length in k we conclude our work showing that units in torsion free supersoluble group algebras are bounded in that the supports of units and their inverses are related through a property u and the induced length function l

volumetric locking issue with uncertainty in the design of locally resonant acoustic metamaterials abstract in the design of locally resonant acoustic metamaterials lrams the incompressible rubber is widely used however the physical behavior of lrams with a ternary structure is very sensitive to the poisson s ratio of incompressible rubber the slight variance of poisson s ratio could lead to a significant change of physical responses of lrams on the other hand the manufacturing error is unavoidable in the application of lrams therefore it is important to predict the upper and lower bounds of physical responses of lrams with uncertainty parameters for the first time the mathematical model to predict the upper and lower bounds of mechanical response of lrams with uncertainty parameters such as young s modulus poisson s ratio and density is established by the nonlinear interval perturbation hybrid node based smoothed finite element method niph ns fem one of the main features of niph ns fem with a softened effect in the discretized model is capable to overcome the volumetric locking issue of incompressible rubber in the standard finite element method fem the accuracy and effectiveness of niph ns fem have been validated by two numerical examples including lrams with binary and ternary structures

a polynomial expansion approach for response analysis of periodical composite structural acoustic problems with multi scale mixed aleatory and epistemic uncertainties abstract the response analysis of periodical composite structural acoustic problem with multi scale mixed aleatory and epistemic uncertainties is investigated based on homogenization method in this paper the aleatory uncertainties are presented by bounded random variables whereas the epistemic uncertainties are presented by interval variables and evidence variables when dealing with the combination of bounded random variables interval variables and evidence variables enormous computation is needed to estimate the output probability bounds of the sound pressure response of the periodical composite structural acoustic system to reduce the involved computational cost but without losing accuracy by transforming all of the bounded random variables and interval variables into evidence variables appropriately an evidence theory based polynomial expansion method epem is developed in which the gegenbauer series expansion is employed to approximate the variation range of the response with respect to evidence variables by using epem the probability bounds of the response can be obtained efficiently a numerical example is used to validate the proposed method and two engineering examples are given to demonstrate its efficiency

polyhedral norms on non separable banach spaces abstract we prove the existence of equivalent polyhedral norms on a number of classes of non separable spaces the majority of which being of the form c k in particular we obtain a complete characterization of those trees t such that c 0 t admits an equivalent polyhedral norm

on weakly locally uniformly rotund banach spaces abstract we show that every normed space e with a weakly locally uniformly rotund norm has an equivalent locally uniformly rotund norm after obtaining a discrete network of the unit sphere s e for the weak topology we deduce that the space e must have a countable cover by sets of small local diameter which in turn implies the renorming conclusion this solves a question posed by deville godefroy haydon and zizler for a weakly uniformly rotund norm we prove that the unit sphere is always metrizable for the weak topology despite the fact that it may not have the kadec property moreover banach spaces having a countable cover by sets of small local diameter coincide with the descriptive banach spaces studied by hansell so we present here some new characterizations of them

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

non probabilistic reliability based topology optimization of geometrically nonlinear structures using convex models this paper describes a non probabilistic reliability based topology optimization method for the design of continuum structures undergoing large deformations the variation of the structural system is treated with the multi ellipsoid convex model which is a realistic description of the parameters being inherently uncertain but bounded or lacking sufficient probabilistic data the formulation of the optimal design is established as a volume minimization problem with non probabilistic reliability constraints on the geometrically nonlinear structural behaviour in order to circumvent numerical difficulties in solving the nested double loop optimization problem a performance measure based approach is employed to transform the constraint on the reliability index into one on the concerned performance in conjunction with an efficient adjoint variable scheme for the sensitivity analysis of reliability constraints the optimization problem is solved by gradient based mathematical programming methods three numerical examples for the optimization design of planar structures are presented to illustrate the validity and applicability of the proposed method the obtained optimal solutions show the importance of incorporating various uncertainties in the design problem moreover it is also revealed that the geometrical nonlinearity needs to be accounted for to ensure satisfaction of the reliability constraints in the optimal design of structures with large deformation

modal analysis of structures with uncertain but bounded parameters via interval analysis in this paper the modal interval analysis method to estimate modal parameters frequency response function frf and mode shapes of structures with uncertain but bounded is presented although the system parameters or properties are uncertain in many engineering problems but their probable range of values i e upper and lower bounds can be provided from practical experience and engineering knowledge moreover to avoid the resonance of a structure and to consider the dynamic response of an uncertain one and also for reliability and stability analysis we often need the bounds of the ranges of structural characteristic parameters such as natural frequency and normal mode by using modal analysis and interval calculus we investigate the method of computing upper and lower bounds of paramenters such as natural frequencies modal shapes and frfs theoretically it is possible to analyze the uncertain but bounded of a structure by using modal analysis and interval calculus they can be estimated by modal interval analysis on the basis of the estimated intervals the engineering structure parameters can be applied into engineering design a numerical example is presented for a tower structure and the results illustrate that the proposed method is effective a comparison of the modal interval method with the results of monte carlo simulation serves to validate the solutions and to identify the bounded ranges of parameters

hybrid uncertainty propagation in structural acoustic systems based on the polynomial chaos expansion and dimension wise analysis abstract hybrid uncertainties are ubiquitous in the structural acoustic analysis and greatly affect the behaviors of the coupled system however requirements of small uncertainties and rewriting simulation codes for the numerical analysis are always necessary for current methods in this context a non intrusive dual layer analysis procedure i e a hybrid method of the polynomial chaos expansion and dimension wise analysis pce dw is proposed in this paper the pce procedure based on the sparse grid collocation strategy is utilized to handle the random uncertainty while the dw procedure is employed to evaluate the interval bounds of statistical characteristics of the system response the pce dw also applies to the structural acoustic analysis with only random or interval parameters the investigation of two structural acoustic systems with hybrid uncertainties finally demonstrates the accuracy efficiency and capability of the proposed method

some applications of projective resolutions of identity we show that the unit ball k of the bidual of an asplund space is a corson compact or contains 0 1 and that it has the namioka property on separate to joint continuity the same results are shown for k a valdivia compact a by product is that all dyadic compacts have the namioka property some connections with weakly compactly generated dual spaces and renormings are given

unified polynomial expansion for interval and random response analysis of uncertain structure acoustic system with arbitrary probability distribution abstract for structure acousticsystem with uncertainties the interval model the random model and the hybrid uncertain model have been introduced in the interval model and the random model the uncertain parameters are described as either the random variable with well defined probability density function pdf or the interval variable without any probability information whereas in the hybrid uncertain model both interval variable and random variable exist simultaneously for response analysis of these three uncertain models of structure acoustic problem involving arbitrary pdfs a unified polynomial expansion method named as the interval and random arbitrary polynomial chaos method irapcm is proposed in irapcm the response of the structure acoustic system is approximated by apc expansion in a unified form particularly only the weight function of polynomial basis is required to be changed to construct the apc expansion for the response of different uncertain models through the unified apc expansion the uncertain properties of the response of three uncertain models can be efficiently obtained as the apc expansion can provide a free choice of the polynomial basis the optimal polynomial basis for the random variable with arbitrary pdfs can be obtained by using the proposed irapcm the irapcm has been employed to solve a mathematical problem and a structure acoustic problem and the effectiveness of the unified irapcm for response analysis of three uncertain models is demonstrated by fully comparing it with the hybrid first order perturbation method and several existing polynomial chaos methods

stochastic hybrid perturbation technique based smoothed finite element statistical energy method for mid frequency analysis of structure acoustic systems with parametric and nonparametric uncertainties abstract at present the most widely used mid frequency method i e the hybrid finite element statistical energy analysis method fe sea still holds potential flaws e g low accuracy and ignoring uncertain factors in order to eliminate these problems a generalized smoothing finite element statistical energy analysis method sfe sea is first proposed in this work which is constructed based on the edge based gradient smoothing technique thus reducing the dispersion error in the deterministic calculations second on the basis of the proposed sfe sea the parametric uncertainty models will be introduced combining the second order random interval perturbation method and the random interval moment method etc thus a mid frequency analysis method shpsfem sea considering both parametric uncertainties both the random and interval variables and nonparametric uncertainties is proposed to effectively analyze the probability and interval characteristics of the random structural acoustic coupled systems moreover for the interval parameters with wide variation range the subinterval perturbation method s shpsfem sea is introduced by dividing the large interval parameters into small interval parameters the proposed methods are compared with the monte carlo simulations of the hybrid fe sea model the high accuracy and efficiency of the proposed methods are verified by two numerical examples

hybrid uncertain static analysis with random and interval fields abstract uncertain static analysis of an engineering structure with diverse type of non deterministic system parameter is investigated in this study unlike the traditional hybrid uncertain static analysis involving random and interval variables the concept of random and interval fields has been implemented to model the spatially dependent uncertainties associated with the system inputs a novel computational approach namely the extended unified interval stochastic sampling x uiss method is proposed to calculate the statistical characteristics i e mean and standard deviation of the extreme bounds i e lower and upper bounds of the concerned responses e g displacement and stress of engineering structure involving hybrid spatially dependent uncertainties subsequently by utilizing either parametric or nonparametric statistical analysis the probability density functions pdfs as well as the cumulative distribution functions cdfs of the extreme bounds of the concerned structural responses can be effectively established consequently the upper and lower bounds of either the concerned responses of the engineering structure at any particular percentile of probability or the structural reliability against any specified capacities can be effectively secured the applicability and effectiveness of the proposed computational analysis framework are illustrated through the numerical investigations on various examples

interval analysis of structures with uncertain but bounded axial stiffness abstract a method to evaluate the static response of structures with interval axial stiffnesses is proposed the procedure overcomes the drawbacks arising in traditional interval analysis due to dependency phenomenon the inversion of the interval stiffness matrix is pursued by means of a novel approximate relationship based on an interval valued sherman morrison woodbury formula numerical results on truss and frame structures evidence the accuracy and the effectiveness of the proposed approach to evaluate bounds of displacements and internal forces

homogenization based interval analysis for structural acoustic problem involving periodical composites and multi scale uncertain but bounded parameters this paper presents a homogenization based interval analysis method for the prediction of coupled structural acoustic systems involving periodical composites and multi scale uncertain but bounded parameters in the structural acoustic system the macro plate structure is assumed to be composed of a periodically uniform microstructure the equivalent macro material properties of the microstructure are computed using the homogenization method by integrating the first order taylor expansion interval analysis method with the homogenization based finite element method a homogenization based interval finite element method hifem is developed to solve a periodical composite structural acoustic system with multi scale uncertain but bounded parameters the corresponding formulations of the hifem are deduced a subinterval technique is also introduced into the hifem for higher accuracy numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented method for a periodical composite structural acoustic system with multi scale uncertain but bounded parameters

a bayesian approach to sound source reconstruction optimal basis regularization and focusing the reconstruction of acoustical sources from discrete field measurements is a difficult inverse problem that has been approached in different ways classical methods beamforming near field acoustical holography inverse boundary elements wave superposition equivalent sources etc all consist implicitly or explicitly in interpolating the measurements onto some spatial functions whose propagation are known and in reconstructing the source field by retropropagation this raises the fundamental question as whether for a given source topology and array geometry there exists an optimal interpolation basis which minimizes the reconstruction error this paper provides a general answer to this question by proceeding from a bayesian formulation that is ideally suited to combining information of physical and probabilistic natures the main findings are the followings 1 the optimal basis functions are the m eigen functions of a specific continuous discrete propagation operator with m being the number of microphones in the array 2 the a priori inclusion of spatial information on the source field causes super resolution according to a phenomenon coined bayesian focusing 3 the approach is naturally endowed with an internal regularization mechanism and results in a robust regularization criterion with no more than one minimum 4 it admits classical methods as particular cases

modified sub interval perturbation finite element method for 2d acoustic field prediction with large uncertain but bounded parameters abstract based on the sub interval perturbation analysis a modified sub interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2d acoustic field with large uncertain but bounded parameters in the proposed method the inversion of the invertible sub interval dynamic stiffness matrix is approximated by a modified approximate interval value sherman morrison woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in neumann series the modified sub interval perturbation procedures are implemented in a numerical finite element framework numerical results on a 2d acoustic tube and a 2d acoustic cavity of a car with large uncertain but bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method

interval and random analysis for structure acoustic systems with large uncertain but bounded parameters abstract for the response analysis of the structure acoustic system with uncertain but bounded parameters three bounded uncertain models are introduced one is the bounded random model in which all of the uncertain but bounded parameters are described as bounded random variables with well defined probability distribution the second one is the interval model in which all of the uncertain but bounded parameters are described as interval variables due to the limited information the third one is the bounded hybrid uncertain model in which the interval variables and the bounded random variables exist simultaneously based on the parametric gegenbauer polynomial which is formulated for bounded random model recently the gegenbauer series expansion method gsem is developed for the response prediction of the structure acoustic system under these three bounded uncertain models within gsem the response of these three bounded uncertain models of the structure acoustic system can be approximated by the unified gegenbauer series with different values of polynomial parameter then the interval and random analysis for these three bounded uncertain models of the structure acoustic system are conducted on the basis of gegenbauer series owing to the orthogonal property of gegenbauer polynomial the analytical solution of the expectation and variance of gegenbauer series with respect to the bounded random variables can be readily obtained the bounds of gegenbauer series with respect to the interval variables are determined by the monte carlo simulation the gsem is applied to solve a shell structure acoustic system under these three bounded uncertain models inspired by the convergence behavior of gsem the relative improvement criterion is established to estimate the required retained order of gegenbauer series for large uncertain problems the results on numerical examples show that gsem with the estimated retained order can achieve a prescribed accuracy and good efficiency for structure acoustic systems with large uncertain but bounded parameters