paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

torsion of a micropolar elastic prism of square cross section abstract an analytical solution is presented for the problem of torsion of a prismatical bar of square cross section of a micropolar cosserat elastic solid warp of the cross sections is found to differ from the warp in a classically elastic solid contrary to the classical case a non zero shear strain is predicted to occur at the edge of the bar novel experimental modalities are suggested on the basis of this analytical solution

facilitating the gibbs sampler the gibbs stopper and the griddy gibbs sampler abstract the article briefly reviews the history literature and form of the gibbs sampler an importance sampling device is proposed for converting the output of the gibbs sampler to a sample from the exact posterior this gibbs stopper technique is also useful for assessing convergence of the gibbs sampler for moderate sized problems also presented is an approach for implementing the gibbs sampler in nonconjugate situations the basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation questions relating to the number of nodes in the approximation gap size between successive nodes and the treatment of unbounded intervals for a given conditional are discussed the methodology is illustrated using a genetic linkage model a nonlinear regression model and the cox model

localisation in a cosserat continuum under static and dynamic loading conditions abstract localisation studies have been carried out for an unconstrained elasto plastic strain softening cosserat continuum because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement a finite constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions because of the existence of rotational degrees of freedom in a cosserat continuum additional wave types arise and wave propagation becomes dispersive this has been investigated analytically and numerically for an elastic cosserat continuum and an excellent agreement has been found between both solutions

bayesian inference and life testing plan for the weibull distribution in presence of progressive censoring this article deals with the bayesian inference of unknown parameters of the progressively censored weibull distribution it is well known that for a weibull distribution while computing the bayes estimates the continuous conjugate joint prior distribution of the shape and scale parameters does not exist in this article it is assumed that the shape parameter has a log concave prior density function and for the given shape parameter the scale parameter has a conjugate prior distribution as expected when the shape parameter is unknown the closed form expressions of the bayes estimators cannot be obtained we use lindley s approximation to compute the bayes estimates and the gibbs sampling procedure to calculate the credible intervals for given priors we also provide a methodology to compare two different censoring schemes and thus find the optimal bayesian censoring scheme monte carlo simulations are performed to observe the behavior of the proposed methods and a data analysis is onducted for ill

a hierarchical bayesian statistical framework for response time distributions this paper provides a statistical framework for estimating higher order characteristics of the response time distribution such as the scale variability and shape consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology e g luce 1986 rt distribution for a single participant depends on certain participant characteristics which in turn can be thought of as arising from a distribution of latent variables the present work focuses on the three parameter weibull distribution with parameters for shape scale and shift initial value bayesian estimation in a hierarchical framework is conceptually straightforward parameter estimates both for participant quantities and population parameters are obtained through markov chain monte carlo methods the methods are illustrated with an application to response time data in an absolute identification task the behavior of the bayes estimates are compared to maximum likelihood ml estimates through monte carlo simulations for small sample size there is an occasional tendency for the ml estimates to be unreasonably extreme in contrast by borrowing strength across participants bayes estimation shrinks extreme estimates the results are that the bayes estimators are more accurate than the corresponding ml estimators

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

non linear elastic micro dilatation theory matrix exponential function paradigm abstract in the present paper the micro dilatation theory or void elasticity is extended to both large displacement and large dilatation firstly the deformation gradient tensor has been freshly defined by means of the matrix exponential function the newly defined relation for the deformation gradient has painstakingly investigated for the uniqueness decomposition issues as well as objectivity and isotropy considerations the relation of the displacement gradient and deformation gradient tensor is brought via the matrix logarithm function the micro dilatation theory constitutive laws are derived using the thermodynamic principles under the zero centrosymmetric weakly centrosymmetric and fully centrosymmetric cases these cases have been derived and scrutinized by the numerical experiments to achieve this assignment the basic loadings are taken into account e g the hydrostatic loading simple traction and shear some conclusions and outlook pertaining to the above mentioned cases and variable bulk density have thereafter discussed

asymptotic analysis of heterogeneous cosserat media abstract the present work deals with the development of homogenization procedures for periodic heterogeneous linear elastic cosserat media it is resorted to asymptotic methods classically used in periodic homogenization it is shown that the nature of the homogeneous equivalent medium depends on the hierarchy of three characteristic lengths the size l of the heterogeneities the cosserat intrinsic lengths l c of the constituents and the typical size l of the considered structure when l and l c are comparable and much smaller than l the effective medium is proved to be a cauchy continuum with volume couples whereas the case l c l leads to a cosserat effective medium finite element simulations are provided in the case of a fiber matrix composite for a large range of characteristic lengths l c and for two different volume fractions reference calculations involving every heterogeneity are compared to the response obtained using a homogeneous equivalent medium the results confirm the predicted hierarchy of models and also show that a cosserat effective medium still provide a good estimation when all characteristic lengths have the same order of magnitude

on various weak fuzzy pairwise retracts the notion of a fuzzy retract was introduced by rodabaugh j math anal appl 79 1981 273 and this notion was extended to the fuzzy bitopological setting j fuzzy math 9 1 2001 207 in this paper we define the notions of fuzzy pairwise semiretracts fuzzy pairwise preretracts fuzzy pairwise strongly semiretracts fuzzy pairwise less strongly semiretracts and fuzzy pairwise semi preretracts we establish some properties of these concepts moreover the relations between these new concepts are discussed

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

use of couple stress theory in elasto plasticity one way to avoid vanishing dissipative energy and localization to zero volume when examining localization and softening problems is to introduce an internal length scale for the material by means of couple stress theory here the constrained cosserat theory is adopted where the displacement field also determines the rotation field for this constrained cosserat theory an elasto plastic theory is derived within a thermodynamic framework and it is shown that the evolution laws for the internal variables can be derived from the postulate of maximum dissipation a generalization of the classical von mises material is proposed both the derivation of the model and the numerical treatment of the integration problem are discussed the generalized von mises model is used in finite element calculations where shear band formation is considered and the results turn out to be independent of the mesh spacing

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

subgrid interaction and micro randomness novel invariance requirements in infinitesimal gradient elasticity abstract we present a micromechanically motivated form of the curvature energy in infinitesimal isotropic gradient elasticity the basis is a homogenization averaging scheme using a micro randomness assumption imposed on a directional higher gradient interaction term these directional interaction terms are matrix valued allowing to apply the standard orthogonal cartan lie algebra decomposition averaging over all subgrid directions leads to three quadratic curvature terms which are conformally invariant when neglecting volumetric effects restricted to rotational inhomogeneities we motivate thereby a symmetric couple stress tensor in the infinitesimal indeterminate couple stress model of koiter mindlin toupin type relations are established to a novel conformally invariant linear cosserat model

on vectorially parameterized natural strain measures of the non linear cosserat continuum the natural lagrangian stretch and wryness tensors of the non linear cosserat continuum are expressed in terms of the general finite rotation vector these expressions are then specialized for seven particular definitions of the rotation vectors known in the literature it is expected that some of the vectorially parameterized strain measures derived here may be more convenient than others in specific applications

a first regularity result for the armstrong frederick cyclic hardening plasticity model with cosserat effects abstract the purpose of this article is to prove the holder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic rate independent armstrong frederick cyclic hardening plasticity model with cosserat effects this model is of non monotone and non associated type in the case of two space dimensions we use the hole filling technique of widman and morrey s dirichlet growth theorem

bayesian analysis for the poly weibull distribution abstract in this article bayesian analysis for a poly weibull distribution using informative priors is discussed this distribution typically arises when the data is the minimum of several weibull failure times from competing risks to perform the bayesian computations simulation using the gibbs sampler is suggested this can be used to find posterior moments the marginal posterior probability density function and the predictive risk or reliability

localized failure analysis in elastoplastic cosserat continua this paper summarizes our experience with localized failure analysis in micropolar cosserat continua the main intent is to examine the regularization properties of discontinuous bifurcation problems when higher grade micropolar materials that exhibit an internal length scale are introduced thereby the key feature is the endowment of micropolar continua with rotational drilling degrees of freedom in addition to the traditional description of motion in terms of displacements after a brief review of elastoplastic cosserat continua we examine recent findings of localization analysis of discontinuous bifurcation 1 to this end we generalize the strength concept of the mohr envelope condition to non symmetric stress states to analyze the localization condition of discontinuous failure 2 the mohr representation of stress leads to a geometrical condition which is used to determine critical hardening softening moduli and localization directions that characterize the particular mode of failure this geometric interpretation of the localization condition lends itself to a systematic study of regularizing weak discontinuities within elastoplastic cosserat continua for illustration of these theoretical findings numerical failure studies are carried out on a representative volume element made of j2 type elastoplastic cosserat material the computational failure simulations demonstrate the non local character of cosserat continua that depends on an internal length scale and on the degree of non symmetry in the stress and strain states the computational results also illustrate the conversion of the underlying failure mode from mixed mode to mode i type failure of decohesion and separation

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on natural strain measures of the non linear micropolar continuum we discuss three different ways of defining the strain measures in the non linear micropolar continuum a by a direct geometric approach b considering the strain measures as the fields required by the structure of local equilibrium conditions and c requiring the strain energy density of the polar elastic body to satisfy the principle of invariance under superposed rigid body deformations the geometric approach a generates several two point deformation measures as well as some lagrangian and eulerian strain measures the ways b and c allow one to choose those lagrangian strain measures which satisfy the additional mechanical requirements these uniquely selected relative strain measures are called the natural ones all the strain measures discussed here are formulated in the general coordinate free form they are valid for unrestricted translations stretches and changes of orientations of the micropolar body and are required to identically vanish in the absence of deformation the relation of the lagrangian stretch and wryness tensors derived here to the ones proposed in the literature is thoroughly discussed

some remarks on lo rs fuzzy compactness abstract in this paper we define lo rs fuzzy compact fuzzy sets we study some properties of lo rs fuzzy compact spaces and lo rs fuzzy compact fuzzy sets we give some characterizations of these notions by fuzzy regularly open sets and fuzzy regularly closed sets we prove that lo rs fuzzy compactness is preserved under a fuzzy almost continuous and fuzzy almost open mapping

a micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity the aim of this work is to formulate a geometrically exact theory of finite deformation and finite rotation micropolar elastoplasticity to obtain a generalized nonlinear continuum framework to this end the classical deformation map is supplemented by an independent rotation field to yield an enhanced configuration space thereby the rotational part of the formulation is consequently parameterized in terms of the rotation pseudo vector via the euler rodrigues formula then micropolar hyperelasticity and multiplicative elastoplasticity are conceptionally derived as in the classical boltzmann continuum the proposed theory is consequently developed in a modern geometry oriented fashion linearization of the kinematics retrofits the well known structure of the micropolar geometrically linear theory

infinitesimal elastic plastic cosserat micropolar theory modelling and global existence in the rate independent case in this article we investigate the regularizing properties of generalized continua of cosserat micropolar type in the elasto plastic case we propose an extension of classical infinitesimal elasto plasticity to include consistently non dissipative micropolar effects it is shown that the new model is thermodynamically admissible and allows for a unique global in time solution of the corresponding rate independent initial boundary value problem the method of choice is the yosida approximation and a passage to the limit

size effect method application for modeling of human cancellous bone using geometrically exact cosserat elasticity abstract in the present study the method of size effect was used to describe the hierarchical multi scale behavior of trabecular human bone using micro ct image the micro ct images extracted from a 98 year old male patient were used to provide the 3d model of cancellous bone which involves one of the most complex natural pore network the non linear or so called geometrically exact cosserat elasticity including augmented lagrangian eulerian ale method has been used to handle the multi scale behavior of trabecular human bone involving size effect in explicit manner we have chosen the conformal energy density within micro randomness issue in which the heterogeneous deformations at small scales are inherently sustained

fuzzy s continuous functions and semilocally connected fuzzy topological spaces abstract the concept of s continuous functions kohli 1978 is translated in fuzzy setting into two concepts fuzzy s continuous functions and fuzzy os continuous functions the concepts of semiconnected functions kohli 1978 and semilocally connected spaces kohli 1978 do the same interactions between those concepts in fuzzy setting and fuzzy continuity chang 1968 are discussed also characterizations of semilocally connected and semilocally o connected fuzzy topological spaces in terms of fuzzy s continuous functions and fuzzy os continuous functions respectively are obtained

existence of minimizers for a finite strain micromorphic elastic solid we investigate geometrically exact generalized continua of micromorphic type in the sense of eringen the two field problem for the macrodeformation and the affine microdeformation p gl 3 r in the quasistatic conservative load case is investigated in a variational form depending on material constants two existence theorems in sobolev spaces are given for the resulting nonlinear boundary value problems these results comprise existence results for the micro incompressible case p sl 3 r and the cosserat micropolar case p so 3 r in order to treat external loads a new condition called bounded external work has to be included which overcomes the conditional coercivity of the formulation the possible lack of coercivity is related to fracture of the micromorphic solid the mathematical analysis uses an extended korn first inequality the methods of choice are the direct methods of the calculus of variations

the performance of the two component extreme value distribution in regional flood frequency analysis the performance of the regional two component extreme value tcev estimation procedure in estimating both dimensionless regional frequency curves showing the t year flood as a multiple of the mean annual flood and site curves incorporating local and regional information was assessed using computer simulation experiments it was found that the tcev procedure produces estimates of both dimensionless regional curves and scaled site quantiles that are relatively unbiased but very variable when data are drawn from tcev or wakeby parents although estimates are very biased when data follow a gev distribution the tcev procedure is robust in the sense that its worst efforts are less bad than those of the alternatives considered but performance declines significantly as sample sizes reduce

a generalized norton hoff model and the prandtl reuss law of plasticity the aim of this article is to study the quasistatic evolution of a three dimensional elastic perfectly plastic solid which satisfies the prandtl reuss law the evolution of the field of stresses which solves a time dependent variational inequality and that of the field of displacements u have been described in previous works 15 26 35 36 37 but it was not shown there that and u satisfy indeed the prandtl reuss constitutive law in this article we find and u in a class of functions which are sufficiently regular for the prandtl reuss law to make sense and we prove that and u satisfy the constitutive law this result is attained by considering the elastic perfectly plastic model as the limit of a family of elastic visco plastic models like those of norton and hoff the norton hoff type models which we introduce depend on a viscosity parameter 0 we study the perturbed models i e 0 fixed and then we pass to the limit 0

analysis of cosserat materials with voronoi cell finite element method and parametric variational principle abstract the elastic plastic analysis of heterogeneous cosserat materials is carried out with the voronoi cell finite element method vcfem under small deformation the parametric complementary energy principle of the cosserat theory is developed by using the parametric variational principle the quadratic programming model and finite element formulation for the vcfem are established compared with the conventional finite element method fem the newly developed method requires no tedious iterative procedures and has no convergence problems based on the developed method the influence of microscopic heterogeneities on the overall mechanical responses of heterogeneous materials is studied numerical examples are given to demonstrate the validity and efficiency of the method developed

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

fuzzy path and fuzzy connectedness abstract this paper discusses fuzzy connectedness in fuzzy topology zadeh s classical paper 1 has introduced the fundamental concept of a fuzzy set upon which the foundation of fuzzy mathematics rests the theory of fuzzy topology is a branch of such mathematics our purpose is to introduce some basic concepts as fuzzy path fuzzy path connected set locally fuzzy path connected set in the fuzzy topological spaces and to prove some fundamental properties related to fuzzy connectedness

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

enhanced numerical study of infinitesimal non linear cosserat theory based on the grain size length scale assumption abstract a non linear cosserat theory involving the arbitrary lagrangian eulerian ale method has been introduced into the brittle isotropic materials amorphous glass and cement mortar using the modified brazilian disk mbd under an uni axial compressive loading these numerical experiments shed light on the nature of the cosserat based media and material moduli determination which are difficult to acquire using the most well known experimental viewpoints by using the identical micro rotation constants l g 2 and 2 3 the cosserat moduli reduce to only four constants for the 3d cases according to the results obtained in this paper the present methodology substantiates that the cosserat theory would be readily applied to the wide range of materials from the full amorphous materials to the heterogeneous materials by changing the length scale parameter some fresh routes and new outlooks are discussed afterwards

the armstrong frederick cyclic hardening plasticity model with cosserat effects abstract we propose an extension of the cyclic hardening plasticity model formulated by armstrong and frederick which includes micropolar effects our micropolar extension establishes coercivity of the model which is otherwise not present we study then existence of solutions to the quasistatic rate independent armstrong frederick model with cosserat effects which is however still of non monotone non associated type in order to do this we need to relax the pointwise definition of the flow rule into a suitable weak energy type inequality it is shown that the limit in the yosida approximation process satisfies this new solution concept the limit functions have a better regularity than previously known in the literature where the original armstrong frederick model has been studied