a stream virtual element formulation of the stokes problem on polygonal meshes in this paper we propose and analyze a novel stream formulation of the virtual element method vem for the solution of the stokes problem the new formulation hinges upon the introduction of a suitable stream function space characterizing the divergence free subspace of discrete velocities and it is equivalent to the velocity pressure inf sup stable mimetic scheme presented in l beirao da veiga et al j comput phys 228 2009 pp 7215 7232 up to a suitable reformulation into the vem framework both schemes are thus stable and linearly convergent but the new method results to be more desirable as it employs much less degrees of freedom and it is based on a positive definite algebraic problem several numerical experiments assess the convergence properties of the new method and show its computational advantages with respect to the mimetic one

finite element approximations of a ladyzhenskaya model for stationary incompressible viscous flow some finite element approximation procedures are presented for a model proposed by ladyzhenskaya for stationary incompressible viscous flow the approximate problems are proved to be well posed and stable under standard assumptions on the finite element families the solutions of the approximate problems converge to the solution of the original problem under minimum regularity assumptions some error estimates are derived the optimal order of accuracy is assured with or even without using exact integration rules in the approximation procedure iterative methods for solving the discrete nonlinear problems and comments on some computational experiments are provided special attention is also paid to the common properties as well as differences between the approximation procedure presented here and the approximation for the stationary navier stokes equations

fuzzy vector spaces abstract this paper defines a basis for a fuzzy vector space and its dimension a class of fuzzy vector spaces having dimension is introduced and two standard results from crisp theory are proved for this case namely d i m e1 e2 d i m e1 d i m e2 d i m e1 e2 and rmd i m i m f d i m k e r f the product of two fuzzy vector spaces under certain conditions is also characterised

a comment on analysis of video image sequences using point and line correspondences abstract in this paper we would like to contest the results of y f wang n karandikar and j k aggarwal pattern recognition 24 1065 1085 1991 raising two fundamental claims a line does not contribute anything to recognition of motion parameters from two images four traceable points are not sufficient to recover motion parameters from two perspective projections to be constructive however we show that four traceable points are sufficient to recover motion parameters from two frames under orthogonal projection and that five points are sufficient to simplify the solution of the two frame problem under orthogonal projection to solving a linear equation system

interpreting image curve from multiframes abstract a method of reconstructing the structure of a rigid space curve from multiframes is presented the problem is formulated as does there exist a unique reconstruction of a general smooth space curve from images if the curve is moving constantly in the space what is the minimum information needed to allow such a reconstruction the motion here is taken to be general but rotates about a fixed axis uniformly the only featured points are the two endpoints of the curve we first establish a necessary and sufficient condition on the number of frames for determining the motion with only two feature points observable also whether the underlying motion meets the formulation of the problem can be checked from the observables next we show that the ambiguities of matching a given nonfeatured point on the curve in one frame are limited to the intersections of a straight line and the image curve on the other frame the ambiguities of matching nonfeature points can then be resolved and the reconstruction of the space curve follows readily experiments and examples are provided to illustrate each step of the method furthermore we find that conclusions obtained by yuille and poggio 8 generalized ordering constraint in the case of parallel projection are either special cases of or can be easily derived from this method

a mixed local discontinuous galerkin method for a class of nonlinear problems in fluid mechanics in this paper we present and analyze a new mixed local discontinuous galerkin ldg method for a class of nonlinear model that appears in quasi newtonian stokes fluids the approach is based on the introduction of the flux and the tensor gradient of the velocity as further unknowns in addition a suitable lagrange multiplier is needed to ensure that the corresponding discrete variational formulation is well posed this yields a two fold saddle point operator equation as the resulting ldg mixed formulation which is then reduced to a dual mixed formulation applying a nonlinear version of the well known babuska brezzi theory we prove that the discrete formulation is well posed and derive the corresponding a priori error analysis we also develop a reliable a posteriori error estimate and propose the associated adaptive algorithm to compute the finite element solutions finally several numerical results illustrate the performance of the method and confirm its capability to localize boundary and inner layers as well as singularities

discontinuous skeletal gradient discretisation methods on polytopal meshes in this work we develop arbitrary order discontinuous skeletal gradient discretisations dsgd on general polytopal meshes discontinuous skeletal refers to the fact that the globally coupled unknowns are broken polynomial on the mesh skeleton the key ingredient is a high order gradient reconstruction composed of two terms i a consistent contribution obtained mimicking an integration by parts formula inside each element and ii a stabilising term for which sufficient design conditions are provided an example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high order residuals on a raviart thomas nedelec subspace we prove that the novel dsgds satisfy coercivity consistency limit conformity and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems links with hybrid high order non conforming mimetic finite difference and non conforming virtual element methods are also studied numerical examples complete the exposition

a dual mixed approximation method for a three field model of a nonlinear generalized stokes problem in this work a dual mixed approximation of a nonlinear generalized stokes problem is studied the problem is analyzed in sobolev spaces which arise naturally in the problem formulation existence and uniqueness results are given and error estimates are derived it is shown that both lowest order and higher order mixed finite elements are suitable for the approximation method numerical experiments that support the theoretical results are presented

estimation of object motion parameters from noisy images an approach is presented for the estimation of object motion parameters based on a sequence of noisy images the problem considered is that of a rigid body undergoing unknown rotational and translational motion the measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points by modeling the object dynamics as a function of time estimates of the model parameters including motion parameters can be extracted from the data using recursive and or batch techniques this permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images some assumptions regarding object structure are presently made results are presented for a recursive estimation procedure the case considered here is that of a sequence of one dimensional images of a two dimensional object thus the object moves in one transverse dimension and in depth preserving the fundamental ambiguity of the central projection image model loss of depth information an iterated extended kalman filter is used for the recursive solution noise levels of 5 10 percent of the object image size are used approximate cramer rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level this approach may be of use in situations where it is difficult to resolve large numbers of object match points but relatively long sequences of images 10 to 20 or more are available

finite element error analysis of a quasi newtonian flow obeying the carreau or power law we consider the finite element approximation of a quasi newtonian flow where the viscosity obeys the carreau or power law for sufficiently regular solutions we prove energy type error bounds for the velocity and pressure these bounds improve on existing results in the literature

a nonconforming virtual element method for the stokes problem on general meshes abstract in this paper a nonconforming virtual element method for the stokes problem is proposed and investigated this method gives a unified scheme for two and three dimensions simultaneously in addition it provides an attractive computational feature treatment of general elements including non convex and degenerate elements moreover by choosing a proper low order velocity and pressure pair we prove the discrete inf sup condition for this method to obtain its solvability and stability furthermore we show optimal energy norm error estimates for velocity and l 2 norm error estimates for both velocity and pressure finally a series of numerical experiments are performed to validate that this method has good stability and accuracy for the stokes problem

a priori and a posteriori error analyses of a high order unfitted mixed fem for stokes flow abstract we propose and analyze a high order unfitted mixed finite element method for the pseudostress velocity formulation of the stokes problem with dirichlet boundary condition on a fluid domain with curved boundary the method consists of approximating by a polyhedral subdomain d h with boundary h where a galerkin method is applied to approximate the solution and on a transferring technique based on integrating the extrapolated discrete gradient of the velocity to approximate the dirichlet boundary data on the computational boundary h the associated galerkin scheme is defined by raviart thomas elements of order k 0 for the pseudostress and discontinuous polynomials of degree k for the velocity provided suitable hypotheses on the mesh near the boundary we prove well posedness of the galerkin scheme by means of the babuska brezzi theory and establish the corresponding optimal convergence of o h k 1 moreover for the case when h is constructed through a piecewise linear interpolation of we propose a reliable and quasi efficient residual based a posteriori error estimator its definition makes use of a postprocessed velocity with enhanced accuracy to achieve the same rate of convergence of the method when the solution is smooth enough numerical experiments illustrate the performance of the scheme show the behavior of the associated adaptive algorithm and validate the theory

fuzzy linear maps the concept of the fuzzy subspace of a space of fuzzy linear maps is defined and investigated also the fuzzy basis of this subspace is determined

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

motion and structure from line correspondences closed form solution uniqueness and optimization this work discusses estimating motion and structure parameters from line correspondences of a rigid scene the authors present a closed form solution to motion and structure parameters from line correspondences through three monocular perspective views the algorithm makes use of redundancy in the data to improve the accuracy of the solutions the uniqueness of the solution is established and necessary and sufficient conditions for degenerate spatial line configurations are given optimization has been employed to further improve the accuracy of the estimates in the presence of noise simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound

motion estimation with more than two frames the development of a general motion estimation system based on using three or more frames is reported the relevant portion of the sequence is treated as a whole thus simplifying the process of estimating the motion parameters and making possible the computation of the motion parameters in terms of the natural center of motion a general description of this motion estimation method is presented with the derivation of motion equations for three cases three points in three frames two points in four frames and one point in five frames results are given for real and synthetic images for the case of one point in five and six frames on the average the program converged quickly to the right answer for noiseless data for noisy data the answers were reasonable and their accuracy was directly a function of the amount of noise in the disparity vector

fuzzy linear and affine spaces abstract elementary properties of fuzzy linear and affine spaces are studied the concept of a basis for a fuzzy linear space is defined and an algorithm for computing a basis when the underlying space is finite dimensional is given

exact sequences of fuzzy linear maps abstract in this paper we study properties of fuzzy linear maps over fuzzy vector spaces as a powerful tool exact sequences of fuzzy linear maps are introduced and a foundational frame of fuzzy homology is established we define a series of important concepts such as fuzzy weak isomorphism the kernel of a fuzzy linear map and quasi monicity and deal with short exact sequences of fuzzy linear maps specially we obtain an analogy of the first isomorphism theorem and discuss split exactness of short sequences of fuzzy linear maps the relations between two short exact sequences of fuzzy linear maps linked by fuzzy linear maps and discuss the stability of some finally we introduce the complex of fuzzy linear maps and discuss the stability of some complexes

analysis of an augmented pseudostress based mixed formulation for a nonlinear brinkman model of porous media flow abstract in this paper we introduce and analyze an augmented mixed finite element method for the two dimensional nonlinear brinkman model of porous media flow with mixed boundary conditions more precisely we extend a previous approach for the respective linear model to the present nonlinear case and employ a dual mixed formulation in which the main unknowns are given by the gradient of the velocity and the pseudostress in this way and similarly as before the original velocity and pressure unknowns are easily recovered through a simple postprocessing in addition since the neumann boundary condition becomes essential we impose it in a weak sense which yields the introduction of the trace of the fluid velocity over the neumann boundary as the associated lagrange multiplier we apply known results from nonlinear functional analysis to prove that the corresponding continuous and discrete schemes are well posed in particular a feasible choice of finite element subspaces is given by raviart thomas elements of order k 0 for the pseudostress piecewise polynomials of degree k for the gradient of the velocity and continuous piecewise polynomials of degree k 1 for the lagrange multiplier we also derive a reliable and efficient residual based a posteriori error estimator for this problem finally several numerical results illustrating the performance and the robustness of the method confirming the theoretical properties of the estimator and showing the behavior of the associated adaptive algorithm are provided

some experiments on estimating the 3 d motion parameters of a rigid body from two consecutive image frames this paper describes the results of some experiments on estimating the 3 d motion parameters of a rigid body from two consecutive tv images and discusses several factors which affect the accuracy of the results these factors include the sizes of the motion parameters themselves the accuracy of the raw data and the number of point correspondences in addition we address two related topics determining corner positions to subpixel accuracy and matching point patterns with different scales

a posteriori error analysis of a mixed virtual element method for a nonlinear brinkman model of porous media flow abstract in this paper we present an a posteriori error analysis of a mixed vem discretization for a nonlinear brinkman model of porous media flow which has been proposed by the authors in a previous work therein the system is formulated in terms of a pseudostress tensor and the velocity gradient whereas the velocity and the pressure of the fluid are computed via postprocessing formulas furthermore the well posedness of the associated augmented formulation along with a priori error bounds for the discrete scheme also were established we now propose reliable and efficient residual based a posteriori error estimates for a computable approximation of the virtual solution associated to the aforementioned problem the resulting error estimator is fully computable from the degrees of freedom of the solutions and applies on very general polygonal meshes for the analysis we make use of a global inf sup condition helmholtz decomposition local approximation properties of interpolation operators and inverse inequalities together with localization arguments based on bubble functions finally we provide some numerical results confirming the properties of our estimator and illustrating the good performance of the associated adaptive algorithm

the nonconforming virtual element method for the stokes equations we present the nonconforming virtual element method vem for the numerical approximation of velocity and pressure in the steady stokes problem the pressure is approximated using discontinuous piecewise polynomials while each component of the velocity is approximated using the nonconforming virtual element space on each mesh element the local virtual space contains the space of polynomials of up to a given degree plus suitable nonpolynomial functions the virtual element functions are implicitly defined as the solution of local poisson problems with polynomial neumann boundary conditions as typical in vem approaches the explicit evaluation of the non polynomial functions is not required this approach makes it possible to construct nonconforming virtual spaces for any polynomial degree regardless of the parity for two and three dimensional problems and for meshes with very general polygonal and polyhedral elements we show that the nonconforming vem is inf sup stable and establish optimal a pri

a discontinuous skeletal method for the viscosity dependent stokes problem we devise and analyze arbitrary order nonconforming methods for the discretization of the viscosity dependent stokes equations on simplicial meshes we keep track explicitly of the viscosity and aim at pressure robust schemes that can deal with the practically relevant case of body forces with large curl free part in a way that the discrete velocity error is not spoiled by large pressures the method is inspired from the recent hybrid high order hho methods for linear elasticity after elimination of the auxiliary variables by static condensation the linear system to be solved involves only discrete face based velocities which are polynomials of degree k ge 0 and cell wise constant pressures our main result is a pressure independent energy error estimate on the velocity of order k 1 the main ingredient to achieve pressure independence is the use of a divergence preserving velocity reconstruction operator in the discretization of the body forces we also prove an l 2 pressure estimate of order k 1 and an l 2 velocity estimate of order k 2 the latter under elliptic regularity the local mass and momentum conservation properties of the discretization are also established finally two and three dimensional numerical results are presented to support the analysis

virtual elements for the navier stokes problem on polygonal meshes a family of virtual element methods for the two dimensional navier stokes equations is proposed and analyzed the schemes provide a discrete velocity field which is pointwise divergence free a ri

fuzzy linear spaces abstract nanda 1986 introduced the concept of fuzzy linear space biswas considered that nanda s definition was not rational and redefined the concept of fuzzy linear space 1989 in this paper we first point out the problems by two counter examples next we redefine the concept of fuzzy field and fuzzy linear space and give some fundamental properties

analysis of a velocity pressure pseudostress formulation for the stationary stokes equations abstract we consider a non standard mixed approach for the stokes problem in which the velocity the pressure and the pseudostress are the main unknowns alternatively the pressure can be eliminated from the original equations thus yielding an equivalent formulation with only two unknowns in this paper we develop a priori and a posteriori error analyses of both approaches we first apply the babuska brezzi theory to prove the well posedness of the continuous and discrete formulations in particular we show that raviart thomas elements of order k 0 for the pseudostresses and piecewise polynomials of degree k for the velocities and the pressures ensure unique solvability and stability of the associated galerkin schemes then we derive reliable and efficient residual based a posteriori error estimators for both schemes without and with pressure unknown finally we provide several numerical results illustrating the good performance of the resulting mixed finite element methods confirming the theoretical properties of the estimators and showing the behaviour of the associated adaptive algorithms

a low order mixed finite element method for a class of quasi newtonian stokes flows part i a priori error analysis abstract this is the second part of a work dealing with a low order mixed finite element method for a class of nonlinear stokes models arising in quasi newtonian fluids in the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation and that the corresponding galerkin scheme becomes well posed with piecewise constant functions and raviart thomas spaces of lowest order as the associated finite element subspaces in this paper we develop a bank weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions several numerical results illustrating the efficiency of the method are also provided

dual mixed finite element approximation of stokes and nonlinear stokes problems using trace free velocity gradients in this work a finite element method for a dual mixed approximation of stokes and nonlinear stokes problems is studied the dual mixed structure which yields a twofold saddle point problem arises in a formulation of this problem through the introduction of unknown variables with relevant physical meaning the method approximates the velocity its gradient and the total stress tensor but avoids the explicit computation of the pressure which can be recovered through a simple postprocessing technique this method improves an existing approach for these problems and uses raviart thomas elements and discontinuous piecewise polynomials for approximating the unknowns existence uniqueness and error results for the method are given and numerical experiments that exhibit the reduced computational cost of this approach are presented

a discontinuous skeletal method for advection diffusion reaction on general meshes we design and analyze an approximation method for advection diffusion reaction equa tions where the generalized degrees of freedom are polynomials of order k 0 at mesh faces the method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions fairly general meshes with poly topal and nonmatching cells are supported arbitrary polynomial orders can be considered including the case k 0 which is closely related to mimetic finite difference mixed hybrid finite volume methods the error analysis covers the full range of peclet numbers including the delicate case of local degeneracy where diffusion vanishes on a strict subset of the domain computational costs remain moderate since the use of face unknowns leads to a compact stencil with reduced communications numerical results are presented

a hybrid high order method for a class of quasi newtonian stokes equations on general meshes abstract in this paper we introduce a hybrid high order hho discrete scheme for numerically solving a class of incompressible quasi newtonian stokes equations in r 2 the presented hho method depends on hybrid discrete velocity unknowns at cells and edges and pressure unknowns at cells benefiting from the hybridization of unknowns the computation cost can be reduced by the technique of static condensation and the solvability of the static condensation algebra system is proved furthermore we study the hho scheme by polynomials of arbitrary degrees k k 1 on the general meshes and geometries the unique solvability of the discrete scheme is proved additionally the optimal a priori error estimates for the velocity gradient and pressure approximations are obtained finally we provide several numerical results to verify the good performance of the proposed hho scheme and confirm the optimal approximation properties on a variety of meshes and geometries

a hybrid high order method for the cahn hilliard problem in mixed form in this work we develop a fully implicit hybrid high order algorithm for the cahn hilliard problem in mixed form the space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces the proposed method has several advantageous features i it supports fairly general meshes possibly containing polyhedral elements and nonmatching interfaces ii it allows arbitrary approximation orders and iii it has a moderate computational cost thanks to the possibility of locally eliminating element based unknowns by static condensation we perform a detailed stability and convergence study proving optimal convergence rates in energy like norms numerical validation is also provided using some of the most common tests in the literature

h text div h div and h mathbf curl h curl conforming virtual element methods in the present paper we construct virtual element spaces that are h mathrm div h div conforming and h mathbf curl h curl conforming on general polygonal and polyhedral elements these spaces can be interpreted as a generalization of well known finite elements we moreover present the basic tools needed to make use of these spaces in the approximation of partial differential equations finally we discuss the construction of exact sequences of vem spaces

a hybrid high order locking free method for linear elasticity on general meshes abstract we devise an arbitrary order locking free method for linear elasticity the method relies on a pure displacement primal formulation and leads to a symmetric positive definite system matrix with compact stencil the degrees of freedom are vector valued polynomials of arbitrary order k 1 on the mesh faces so that in three space dimensions the lowest order scheme only requires 9 degrees of freedom per mesh face the method can be deployed on general polyhedral meshes the key idea is to reconstruct the symmetric gradient and divergence inside each mesh cell in terms of the degrees of freedom by solving inexpensive local problems the discrete problem is assembled cell wise using these operators and a high order stabilization bilinear form locking free error estimates are derived for the energy norm and for the l 2 norm of the displacement with optimal convergence rates of order k 1 and k 2 respectively for smooth solutions on general meshes the theoretical results are confirmed numerically and the cpu cost is evaluated on both standard and polygonal meshes

a priori and a posteriori error analyses of a velocity pseudostress formulation for a class of quasi newtonian stokes flows abstract in this paper we introduce and analyze new mixed finite element schemes for a class of nonlinear stokes models arising in quasi newtonian fluids the methods are based on a non standard mixed approach in which the velocity the pressure and the pseudostress are the original unknowns however we use the incompressibility condition to eliminate the pressure and set the velocity gradient as an auxiliary unknown which yields a twofold saddle point operator equation as the resulting dual mixed variational formulation in addition a suitable augmented version of the latter showing a single saddle point structure is also considered we apply known results from nonlinear functional analysis to prove that the corresponding continuous and discrete schemes are well posed in particular we show that raviart thomas elements of order k 0 for the pseudostress and piecewise polynomials of degree k for the velocity and its gradient ensure the well posedness of the associated galerkin schemes moreover we prove that any finite element subspace of the square integrable tensors can be employed to approximate the velocity gradient in the case of the augmented formulation then we derive a reliable and efficient residual based a posteriori error estimator for each scheme finally we provide several numerical results illustrating the good performance of the resulting mixed finite element methods confirming the theoretical properties of the estimator and showing the behaviour of the associated adaptive algorithms

fuzzy finitely generated modules abstract we introduce the category of fuzzy modules and discuss the construction of fuzzy finitely generated modules characterizations of a sort of fuzzy modules in which the fuzzy value distribution is finite are partly obtained

analysis of video image sequences using point and line correspondences abstract in this research we investigate the problem of analyzing time varying imagery using a feature based approach we assume a scenario where the imaged objects remain stationary while the camera moves the goal is to compute the structure of the imaged objects and the motion of the camera from a sequence of video images the proposed method exploits the principle of the invariance of rigid configurations during motion using the rigidity constraints we specify equations based on distance and angular invariance to compute the structural parameters of the imaged 3d objects independently of the camera s motion once the structural parameters are recovered the motion parameters can be computed the strength of our approach is in the decomposition of the computations of structure and motion and in the use of point and line correspondences simultaneously the main advantage of using both points and lines is that our approach is not limited to objects whose images have only a particular type of feature in abundance in this research we consider the special case of four points and one line which are the minimum feature sets required for computing the structure and motion parameters we then consider additional features in an overdetermined system of equations to improve the reliability and accuracy of the computation we present computer simulation results as well as results from real image sequences to demonstrate the algorithm s validity

the dual of a fuzzy subspace abstract the concept of the dual of a fuzzy subspace is defined double dual fuzzy subspaces and linear maps of fuzzy subspaces are also studied

a posteriori error estimates for the virtual element method an posteriori error analysis for the virtual element method vem applied to general elliptic problems is presented the resulting error estimator is of residual type and applies on very general polygonal polyhedral meshes the estimator is fully computable as it relies only on quantities available from the vem solution namely its degrees of freedom and element wise polynomial projection upper and lower bounds of the error estimator with respect to the vem approximation error are proven the error estimator is used to drive adaptive mesh refinement in a number of test problems mesh adaptation is particularly simple to implement since elements with consecutive co planar edges faces are allowed and therefore locally adapted meshes do not require any local mesh post processing

a posteriori error estimates for a virtual element method for the steklov eigenvalue problem abstract the paper deals with the a posteriori error analysis of a virtual element method for the steklov eigenvalue problem the virtual element method has the advantage of using general polygonal meshes which allows implementing efficiently mesh refinement strategies we introduce a residual type a posteriori error estimator and prove its reliability and global efficiency local efficiency estimates also hold although in some elements they involve boundary terms that are not known to be locally negligible we use the corresponding error estimator to drive an adaptive scheme finally we report the results of a couple of numerical tests that allow us to assess the performance of this approach

using constancy of distance to estimate position and displacement in space the problem of computing structure and motion from the observation of points in two distinct images of a scene is considered the proposed method explicitly utilizes the principle of conservation of distance during rigid body motion the formulation is such that it separates the problem of estimating object position from that of determining motion parameters the equations of invariance of distance for a rigid body are solved for the points position in space when these coordinates in space are known motion parameters are computed in a simple and straightforward manner examples are given to illustrate the efficiency of the algorithm

fuzzy vector spaces abstract let v denote a vector space over a field f and let a denote a fuzzy subspace of v over a fuzzy subfield k of f let x be a fuzzy subset of v such that x a and let x denote the intersection of all fuzzy subspaces of v over k that contain x and are contained in a we characterize the fuzzy subspace x of a over k we use this result to introduce the concept of fuzzy freeness of a fuzzy subset x of v and characterize it in terms of linear independence in the usual sense

bases of fuzzy vector spaces abstract let v be a vector space over a field f let a be a fuzzy subspace of v over f we give sufficient conditions for a to have a basis over a fuzzy subfield k of f we also show that if a has the sup property then a has a fully free basis over f but not necessarily a fully free basis over k

a mixed virtual element method for quasi newtonian stokes flows in this paper we introduce and analyze a virtual element method vem for an augmented mixed variational formulation of a class of nonlinear stokes models arising in quasi newtonian fluids while t

numerical analysis of a three fields model for a quasi newtonian flow abstract we study a finite element approximation of a non linear three fields version of stokes system for incompressible fluids such a problem arises when one considers a white metzner type model for a viscoelastic fluid flow and sets the relaxation time to zero the non linear aspect comes from the fact that a fraction of the viscosity of the fluid depends on the second invariant of the rate of deformation tensor we give existence and unicity results for the continuous problem and its approximation and we prove the error bound

quasi norm error bounds for the finite element approximation of a non newtonian flow we consider the finite element approximation of a non newtonian flow where the viscosity obeys a general law including the carreau or power law for sufficiently regular solutions we prove energy type error bounds for the velocity and pressure these bounds improve on existing results in the literature a key step in the analysis is to prove abstract error bounds initially in a quasi norm which naturally arises in degenerate problems of this type

on pseudo fuzzy linear mappings in this paper we study a more general class of linear maps on fuzzy subsets of vector spaces than those on fuzzy subspaces we obtain a version of the fundamental theorem of homomorphisms which applies to these pseudo fuzzy linear maps in the case of fuzzy subspaces the results become those for fuzzy linear maps we introduce the notion of magnification of pseudo fuzzy linear mappings it is shown that this notion behaves well with respect to the fundamental theorem and with respect to the composition of mapping we note that the class of distribution functions of random variables naturally produces pseudo fuzzy linear mappings which are not fuzzy linear mappings we observe that pseudo fuzzy linear mappings are examples of gain relations we consider general properties of these relations as well as many other examples from these results additional properties of pseudo fuzzy linear mappings are obtained