the robustness of estimates of total indirect effects in covariance structure models estimated by maximum likelihood the large sample distribution of total indirect effects in covariance structure models in well known using monte carlo methods this study examines the applicability of the large sample theory to maximum likelihood estimates oftotal indirect effects in sample sizes of 50 100 200 400 and 800 two models are studied model 1 is a recursive model with observable variables and model 2 is a nonrecursive model with latent variables for the large sample theory to apply the results suggest that sample szes of 200 or more and 400 or more are required for models such as model 1 and model 2 respectively

fuzzy modeling with tolerances abstract we consider the problem of the resolution of fuzzy equation systems a certain number of fuzzy inputs and outputs is given how can we determine a fuzzy relation which describes the behaviour of the object under consideration when attributing this problem to fuzzy equations in the classical sense it may happen that a solution does not exist therefore we introduce fuzzy tolerances as an extension of the solvability conception for this problem we get the whole solution set by means of posets moreover we consider the inverse problem how to determine tolerances to get consistency i e at least one solution for the arising equation system

numerical and applicational aspects of fuzzy relational equations we discuss numerical methods leading to a resolution of fuzzy relational equations which create a formal description of ill defined systems an applicability of the numerical approach is shown in solving some problems in fuzzy systems such as identification and control an idea of fuzzy discretization fuzzy chopping as a meaningful tool for handling various problems is also investigated

some results on the resolution of fuzzy relation equations abstract in this paper two special cases of the solution of the inverse problem are investigated the necessary and sufficient conditions for the existence of a solution such that the upper bound is the unit vector and for a unique solution of the inverse problem equal to the unit vector are presented an algorithmic approach which derives the output vector and the state matrix in each one of these cases is also proposed

resolution of composite interval valued fuzzy relation equations abstract in this study we investigate the properties and the solution procedure of composite interval valued fuzzy relation equations with max min operator this is a generalization of existing constant valued fuzzy relation problems the study includes both theoretical development and numerical analyses it is concluded that our proposed methodology not only solves the existing fuzzy relation equations but also reveals the necessary and sufficient conditions for more general problems therefore this study facilitates the understanding of solution structure and wider applications

a symmetric method for weakly imposing dirichlet boundary conditions in embedded finite element meshes summary in this paper we propose a way to weakly prescribe dirichlet boundary conditions in embedded finite element meshes the key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation relatively small and can be fixed a priori moreover the formulation is symmetric for symmetric problems an additional element discontinuous stress field is used to enforce the boundary conditions in the poisson problem additional terms are required in order to guarantee stability in the convection diffusion equation and the stokes problem the proposed method is then easily extended to the transient navier stokes equations copyright 2012 john wiley sons ltd

the effect of sampling error on convergence improper solutions and goodness of fit indices for maximum likelihood confirmatory factor analysis a monte carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions improper solutions and the distribution of goodness of fit indices in maximum likelihood confirmatory factor analysis nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor effects of practical significance due to sample size the number of indicators per factor and the number of factors were found for gfi agfi and rmr whereas no practical effects were found for the probability values associated with the chi square likelihood ratio test

weakly enforced essential boundary conditions for nurbs embedded and trimmed nurbs geometries on the basis of the finite cell method summary enforcing essential boundary conditions plays a central role in immersed boundary methods nitsche s idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints we formulate an extension of nitsche s method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the b spline and non uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries furthermore we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3d geometries with several benchmark problems we demonstrate the overall good convergence behavior of the proposed method and its good accuracy we provide extensive studies on the stability of the method its influence parameters and numerical properties and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two a newly composed boundary integration concept further enhances the modeling process and allows a flexible discretization independent introduction of boundary conditions finally we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non uniform rational basis spline geometries copyright 2013 john wiley sons ltd

relational equations in totally ordered lattices and their complete resolution abstract the set of all solutions of a composite fuzzy relation equation of sanchez inform and control 30 1976 defined on finite spaces is studied by determining and characterizing all the lower solutions of such an equation

solving interval valued fuzzy relation equations solving systems of fuzzy relation equations is an important topic in fuzzy set theory this paper studies the composite interval valued fuzzy relation equations after analyzing the properties of its solution set we convert the fuzzy relation equations into a fuzzy relation inequality system and propose an efficient computational procedure to generate the whole solution set examples are included to illustrate the idea and algorithm

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

skew symmetric nitsche s formulation in isogeometric analysis dirichlet and symmetry conditions patch coupling and frictionless contact abstract a simple skew symmetric nitsche s formulation is introduced into the framework of isogeometric analysis iga to deal with various problems in small strain elasticity essential boundary conditions symmetry conditions for kirchhoff plates patch coupling in statics and in modal analysis as well as signorini contact conditions for linear boundary or interface conditions the skew symmetric formulation is parameter free for contact conditions it remains stable and accurate for a wide range of the stabilization parameter several numerical tests are performed to illustrate its accuracy stability and convergence performance we investigate particularly the effects introduced by nitsche s coupling including the convergence performance and condition numbers in statics as well as the extra outlier frequencies and corresponding eigenmodes in structural dynamics we present the hertz test the block test and a 3d self contact example showing that the skew symmetric nitsche s formulation is a suitable approach to simulate contact problems in iga

improper solutions in the analysis of covariance structures their interpretability and a comparison of alternate respecifications a monte carlo approach was employed to investigate the interpretability of improper solutions caused by sampling error in maximum likelihood confirmatory factor analysis four models were studied with two sample sizes of the overall goodness of fit indices provided by the lisrel vi program significant differences between improper and proper solutions were found only for the root mean square residual as expected indicators of the factor on which the negative uniqueness estimate occurred had biased loadings and the correlations of its factor with other factors were also biased in contrast the loadings of indicators on other factors and those factor intercorrelations did not have any bias of practical significance for initial solutions with one negative uniqueness estimate three respecifications were studied fix the uniqueness at 00 fix it at 20 or constrain the domain of the solution to be proper for alternate respecified solutions that were converged and proper the constrained solutions and uniqueness fixed at 00 solutions were equivalent the mean goodness of fit and pattern coefficient values for the original improper solutions were not meaningfully different from those obtained under the constrained and uniqueness fixed at 00 respecifications

the asymptotic covariance matrix of maximum likelihood estimates in factor analysis the case of nearly singular matrix of estimates of unique variances this paper is concerned with the asymptotic covariance matrix acm of maximum likelihood estimates mles of factor loadings and unique variances when one element of mles of unique variances is nearly zero i e the matrix of mles of unique variances is nearly singular in this situation standard formulas break down we give explicit formulas for the acm of mles of factor loadings and unique variances that could be used even when an element of mles of unique variances is very close to zero we also discuss an alternative approach using the augmented information matrix under a nearly singular matrix of mles of unique variances and derive the partial derivatives of the alternative constraint functions with respect to the elements of factor loadings and unique variances 2000 elsevier science inc all rights reserved ams classification 62h25 62f12

isogeometric mortar methods the application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically for the lagrange multiplier two choices of uniformly stable spaces are presented both of them are spline spaces but of a different degree in one case we consider an equal order pairing for which a cross point modification based on a local degree reduction is required in the other case the degree of the dual space is reduced by two compared to the primal this pairing is proven to be inf sup stable without any necessary cross point modification several numerical examples confirm the theoretical results and illustrate additional aspects

using phantom and imaginary latent variables to parameterize constraints in linear structural models the most widely used computer programs for structural equation models analysis are the lisrel series of joreskog and sorbom the only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal rindskopf 1983 showed how these simple properties could be used to represent models with more complicated constraints namely inequality constraints on unique variances in this paper two new concepts are introduced which enable a much wider variety of constraints to be made the concepts phantom and imaginary latent variables allow fairly general equality and inequality constraints on factor loadings and structural model coefficients

imposing essential boundary conditions in mesh free methods imposing essential boundary conditions is a key issue in mesh free methods the mesh free interpolation does not verify the kronecker delta property and therefore the imposition of prescribed values is not as straightforward as for the finite element method the aim of this paper is to present a general overview on the existing techniques to enforce essential boundary conditions in galerkin based mesh free methods special attention is paid to the mesh free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of the galerkin weak form particular examples are used to analyze and compare their performance in different situations

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

finite fuzzy relation equations with unique solution in complete brouwerian lattices abstract we characterize finite fuzzy relation equations having a unique solution for sake of completeness we first recall some results already established in foregoing papers in the context of the linear lattices new results are established in the general setting of the complete brouwerian lattices suitable examples illustrate the theorems obtained

three dimensional solid to beam transition elements for structural dynamics analysis complex structural components such as those encountered in many industrial applications may generally be considered as being composed of shell or beam like portions linked to three dimensional solid continua when discretized into finite elements these structures present geometrical and mathematical difficulties at the connections between the different element types since the nodal degrees of freedom allocated to the solid shell and beam elements are incompatible with each other the development of specific and reliable transition finite elements is thus of outstanding practical importance this paper presents efficient c0 compatible transition elements with a variable number of nodes for modelling solid to beam junctions based upon the standard isoparametric solid and beam formulations the current approach includes the properties of both solids and beams verifies the basic continuity smoothness and completeness criteria inherent in the finite element convergence requirements and avoids the shear locking phenomenon typical of c0 elements by using a strain projection method several numerical examples which compare this formulation to analytical and experimental solutions are provided in order to show the applicability and efficiency of this approach

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

on methods for stabilizing constraints over enriched interfaces in elasticity summary enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non smooth problems internal features such as boundaries are represented in such methods by using discontinuous enrichment of the standard finite element basis within such frameworks however imposition of interface constraints and or constitutive relations can cause unexpected difficulties depending upon how relevant fields are interpolated on un gridded interfaces this work address the stabilized treatment of constraints in an enriched finite element context both the lagrange multiplier and penalty enforcement of tied constraints for an arbitrary boundary represented in an enriched finite element context can lead to instabilities and artificial oscillations in the traction fields we demonstrate two alternative variational methods that can be used to enforce the constraints in a stable manner in a bubble stabilized approach fine scale degrees of freedom are added over elements supporting the interface the variational form can be shown to have a similar form to a second approach we consider nitsche s method with the exception that the stabilization terms follow directly from the bubble functions in this work we examine alternative variational methods for enforcing a tied constraint on an enriched interface in the context of two dimensional elasticity we examine several benchmark problems in elasticity and show that only nitsche s method and the bubble stabilization approach produce stable traction fields over internal boundaries we also demonstrate a novel difference between the penalty method and nitsche s method in that the latter passes the patch test exactly regardless of the stabilization parameter s magnitude results for more complicated geometries and triple interface junctions are also presented copyright 2008 john wiley sons ltd

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

local enrichment of nurbs patches using a non intrusive coupling strategy geometric details local refinement inclusion fracture in this work we apply a non intrusive global local coupling strategy for the modelling of local phenomena in a nurbs patch the idea is to consider the nurbs patch to be enriched as the global model this results in a simple flexible strategy first the global nurbs patch remains unchanged which completely eliminates the need for costly re parametrization procedures even if the local domain is expected to evolve then easy merging of a linear nurbs code with any other existing robust codes suitable for the modelling of complex local behaviour is possible the price to pay is the number of iterations of the non intrusive solver but we show that this can be strongly reduced by means of acceleration techniques the main development for nurbs is to be able to handle non conforming geometries only slight changes in the implementation process including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces are made in response to this issue a range of numerical examples in two dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a nurbs patch simply

nitsche s method method for mixed dimensional analysis conforming and non conforming continuum beam and continuum plate coupling a nitche s method is presented to couple dierent mechanical models they include coupling of a solid and a beam and of a solid and a plate both conforming and non conforming formulations are presented in a non conforming formulation the structure domain is overlapped by a rened solid model applications can be found in multi dimensional analyses in which parts of a structure are modeled with solid elements and others are modeled using a coarser model with beam and or plate elements discretisations are performed using both standard lagrange elements and high order nurbs non uniform rational bsplines based isogeometric elements we present various examples to demonstrate the performance of the method

nonconvergence improper solutions and starting values in lisrel maximum likelihood estimation in the framework of a robustness study on maximum likelihood estimation with lisrel three types of problems are dealt with nonconvergence improper solutions and choice of starting values the purpose of the paper is to illustrate why and to what extent these problems are of importance for users of lisrel the ways in which these issues may affect the design and conclusions of robustness research is also discussed

determinants of standard errors of mles in confirmatory factor analysis this paper studies changes of standard errors se of the normal distribution based maximum likelihood estimates mle for confirmatory factor models as model parameters vary using logical analysis simplified formulas and numerical verification monotonic relationships between ses and factor loadings as well as unique variances are found conditions under which monotonic relationships do not exist are also identified such functional relationships allow researchers to better understand the problem when significant factor loading estimates are expected but not obtained and vice versa what will affect the likelihood for heywood cases negative unique variance estimates is also explicit through these relationships empirical findings in the literature are discussed using the obtained results

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

factor analysis with em algorithm never gives improper solutions when sample covariance and initial parameter matrices are proper rubin and thayer psychometrika 47 69 76 1982 proposed the em algorithm for exploratory and confirmatory maximum likelihood factor analysis in this paper we prove the following fact the em algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one when the covariance matrix to be analyzed and the initial matrices including unique variances and inter factor correlations are positive definite we further numerically demonstrate that the em algorithm yields proper solutions for the data which lead the prevailing gradient algorithms for factor analysis to produce improper solutions the numerical studies also show that in real computations with limited numerical precision rubin and thayer s psychometrika 47 69 76 1982 original formulas for confirmatory factor analysis can make factor correlation matrices asymmetric so that the em algorithm fails to converge however this problem can be overcome by using an em algorithm in which the original formulas are replaced by those guaranteeing the symmetry of factor correlation matrices or by formulas used to prove the above fact

on the l2 and the h1 couplings for an overlapping domain decomposition method using lagrange multipliers in this paper a comparison of the l 2 and the h couplings is made for an overlapping domain decomposition method using lagrange multipliers the analysis of the local equations arising from the formulation of the coupling of two mechanical models shows that continuous weight functions are required for the l 2 coupling term whereas both discontinuous and continuous weight functions can be used for the h 1 coupling the choice of the lagrange multiplier space is discussed and numerically studied the paper ends with some numerical examples of an end loaded cantilever beam and a cracked plate under tension and shear it is shown that the continuity enforced with the h 1 coupling leads to a link with a flexibility that can be beneficial for coupling a very coarse mesh with a very fine one to limit the effect of the volume coupling on the global response a narrow coupling zone is recommended in this case volume coupling tends to a surface coupling especially with a l 2 coupling

a two scale model of granular materials a concurrent two scale and two method approach for modeling the mechanical behavior of dry frictional non cohesive granular materials is presented in domains of large eventually discontinuous deformation the material is modeled on the grain scale using a three dimensional discrete element method in the remaining domain the material is considered continuous and modeled by the finite element method using an elasto plastic constitutive equation whose parameters are fit to the particle model via a homogenization scheme the discrete and finite element models are coupled at the interface by the arlequin method an overlapping domain is introduced where the overall virtual work is interpolated between both models and compatibility is assured by kinematic constraints for this purpose the discrete particle displacements are split into a fine and coarse scale part and equality of the coarse scale part and the continuum solution is enforced through the penalty method

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

on direct and inverse problems for fuzzy equation systems with tolerances abstract we investigate the resolution of fuzzy relational equation systems with tolerances which are a certain extension of fuzzy equations considered f i in 3 5 the extension of the concept of higashi and klir 3 enables us to describe the set of solutions to our problem for given tolerances by means of posets in a second part we investigate an inverse problem given upper lower tolerances how to determine lower upper tolerances such that the arising problem becomes consistent numerical examples are given

an embedded mesh method for treating overlapping finite element meshes summary a new technique for treating the mechanical interactions of overlapping finite element meshes is presented such methods can be useful for numerous applications for example fluid solid interaction with a superposed meshed solid on an eulerian background fluid grid in this work we consider the interaction of two elastic domains one mesh is the foreground and defines the surface of interaction the other is a background mesh and is often a structured grid many of the previously proposed methods employ surface defined lagrange multipliers or penalties to enforce the boundary constraints it has become apparent that these methods will cause mesh locking under certain conditions appropriately applied the nitsche method can overcome this locking but in its canonical form is generally not applicable to non linear materials such as hyperelastics the relationship between interior point penalty discontinuous galerkin and nitsche s method is well known based on this relationship a nonlinear theory analogous to the nitsche method is proposed to treat nonlinear materials in an embedded mesh here a discontinuous galerkin derivative based on a lifting of the interface surface integrals provides a consistent treatment for non linear materials and demonstrates good behavior in example problems published 2012 this article is a us government work and is in the public domain in the usa

parameterizing inequality constraints on unique variances in linear structural models current computer programs for analyzing linear structural models will apparently handle only two types of constraints fixed parameters and equality of parameters an important constraint not handled is inequality this is particularly crucial for preventing negative variance estimates in this paper a method is described for imposing several kinds of inequality constraints in models without the necessity for having computer programs which explicitly allow such constraints the examples discussed include the prevention of heywood cases extension to inequalities of parameters to be greater than a specified value and imposing ordered inequalities

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

imposing dirichlet boundary conditions with nitsche s method and spline based finite elements a key challenge while employing non interpolatory basis functions in finite element methods is the robust imposition of dirichlet boundary conditions the current work studies the weak enforcement of such conditions for b spline basis functions with application to both second and fourth order problems this is achieved using concepts borrowed from nitsche s method which is a stabilized method for imposing constraints on surfaces conditions for the stability of the system of equations are derived for each class of problem stability parameters in the nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the dirichlet boundary the approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not through several numerical examples the approach is shown to yield optimal rates of convergence copyright 2010 john wiley sons ltd

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

the arlequin method as a flexible engineering design tool by superposing and gluing models the arlequin method offers an extended modelling framework for the design of engineering structures this paper aims at developing the numerical aspects of the approach and at showing how it can be used with great flexibility and in a consistent manner to change locally a global mechanical model the capabilities of the arlequin method and the effectiveness of the implemented numerical tools are exemplified by 1 d 2 d and 3 d numerical applications

a simple algorithm for obtaining nearly optimal quadrature rules for nurbs based isogeometric analysis we develop new quadrature rules for isogeometric analysis based on the solution of a local nonlinear problem a simple and robust algorithm is developed to determine the rules which are exact for important b spline spaces of uniform and geometrically stretched knot spacings we consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems we find that the rules are almost optimally efficient but much easier to obtain than optimal rules which require the solution of global nonlinear problems that are often ill posed

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure