a nitsche stabilized finite element method for frictional sliding on embedded interfaces part ii intersecting interfaces abstract we extend the weighted nitsche s method proposed in the first part of this study to include multiple intersecting embedded interfaces these intersections arise either inside a computational domain where two internal interfaces intersect or on the boundary of the computational domain where an internal interface intersects with the external boundary we propose a variational treatment of both the interfacial kinematics and the external dirichlet constraints within nitsche s framework we modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the nitsche variational form in the presence of junctions finally we demonstrate the performance of the method for both perfectly tied interfaces and perfectly plastic sliding interfaces through several benchmark examples

on some advanced type inequalities for sugeno integral and t s evaluators in this paper strengthened versions of the minkowski chebyshev jensen and holder inequalities for sugeno integral and t s evaluators are given as an application some equivalent forms and some particular results have been established

stress analysis around crack tips in finite strain problems using the extended finite element method fracture of rubber like materials is still an open problem indeed it deals with modelling issues crack growth law bulk behaviour and computational issues robust crack growth in 2d and 3d incompressibility the present study focuses on the application of the extended finite element method x fem to large strain fracture mechanics for plane stress problems two important issues are investigated the choice of the formulation used to solve the problem and the determination of suitable enrichment functions it is demonstrated that the results obtained with the method are in good agreement with previously published works

symmetry relations in exactly soluble models symmetry relations such as the star triangle or the inverse relation are very useful in determining the partition function of two dimensional exactly soluble models a common construction of the three dimensional equivalents of these symmetry relations is presented they are used to derive in a geometric way applying simultaneously to different kinds of spin models the consequent global properties i e the commutativity of the transfer matrices and the inverse functional equations on the transfer matrix and the partition function the usefulness of the inverse relation is illustrated by an application to the three dimensional ising model

three dimensional integrable models and associated tangle invariants in this paper we show that the boltzmann weights of the three dimensional baxter bazhanov model give representations of the braid group if some suitable spectral limits are taken in the trigonometric case we classify all possible spectral limits which produce braid group representations furthermore we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones

steffensen type inequalities for fuzzy integrals we provide several steffensen type inequalities for the sugeno integral the inequalities are of the form a b f g d a a a f d b or a b f g d a b b f d b where a b are constants is a fuzzy measure on r g a b 0 1 f a b r is nonincreasing or nondecreasing and b a a b g d we show that some of our sufficient conditions are also necessary

general barnes godunova levin type inequalities for sugeno integral integral inequalities play important roles in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure for instance in decision theory the sugeno integral is a median which is indeed a qualitative counterpart to the averaging operation underlying expected utility in this paper barnes godunova levin type inequalities for the sugeno integral on abstract spaces are studied in a rather general form and for this we introduce some new technics for the treatment of concave functions in the sugeno integration context also several examples are given to illustrate the validity of this inequality moreover a strengthened version of barnes godunova levin type inequality for sugeno integrals on a real interval based on a binary operation is presented

a meshless method with enriched weight functions for fatigue crack growth the meshless method is particularly appropriate to solve crack propagation problems in this paper the fatigue growth of cracks in two dimensional bodies is considered the analysis is based upon paris equation new enriched weight functions are introduced in the meshless method formulation to capture the singularity at the crack tip simple problems show the accuracy and efficiency of this method then it is applied to fatigue analysis of single and multi cracked bodies under mixed mode conditions copyright 2004 john wiley sons ltd

a hybrid extended finite element level set method for modeling phase transformations a hybrid numerical method for modelling the evolution of sharp phase interfaces on fixed grids is presented we focus attention on two dimensional solidification problems where the temperature field evolves according to classical heat conduction in two subdomains separated by a moving freezing front the enrichment strategies of the extended finite element method x fem are employed to represent the jump in the temperature gradient that governs the velocity of the phase boundary a new approach with the x fem is suggested for this class of problems whereby the partition of unity is constructed with c1 polynomials and enriched with a c0 function this approach leads to jumps in temperature gradient occurring only at the phase boundary and is shown to significantly improve estimates for the front velocity temporal derivatives of the temperature field in the vicinity of the phase front are obtained with a projection that employs discontinuous enrichment in conjunction with a finer finite difference grid the level set method is used to represent the evolution of the phase interface an iterative procedure is adopted to satisfy the constraints on the temperature field on the phase boundary the robustness and utility of the method is demonstrated with several benchmark problems of phase transformation copyright 2002 john wiley sons ltd

sugeno integral of monotone functions based on lebesgue measure roman flores et al h roman flores a flores franulic y chalco cano the fuzzy integral for monotone functions applied mathematics and computation 185 2007 492 498 gave some optimal upper bounds for the sugeno integral of continuous and strictly monotone functions and provided yong type inequalities for the sugeno integral these results are generalized to monotone functions in this paper two algorithms are given for calculating the sugeno integral of monotone functions based on lebesgue measure several illustrative examples are presented

functional relations and nested bethe ansatz 3 chiral potts model at q 2 1 we obtain the functional relations for the eigenvalues of the transfer matrix of the sl 3 chiral potts model for for the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of bethe ansatz like equations in addition a direct nested bethe ansatz has also been developed for this case

inequalities of the chebyshev type based on pseudo integrals this paper presents the chebyshev type of pseudo integral inequalities with the particular emphasis on the g semirings with the suitable choice of the generator g the pseudo expectation and pseudo moments exist for the cauchy distribution in general case the standard expectation and moments for the cauchy distribution are not defined the computation of the pseudo expectation for the cauchy distribution and some examples that illustrate the applicability of the introduced generalization are also given in the paper

on zamolodchikov s solution of the tetrahedron equations the tetrahedron equations arise in field theory as the condition for thes matrix in 2 1 dimensions to be factorizable and in statistical mechanics as the condition that the transfer matrices of three dimensional models commute zamolodchikov has proposed what appear from numerical evidence and special cases to be non trivial particular solutions of these equations but has not fully verified them here it is proved that they are indeed solutions

holder and minkowski type inequalities for pseudo integral abstract there are proven generalizations of the holder s and minkowski s inequalities for the pseudo integral there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g the second semiring a b sup where is generated and the third semiring where both pseudo operations are idempotent i e sup and inf

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

the vertex formulation of the bazhanov baxter model in this paper we formulate an integrable model on the simple cubic lattice then valued spin variables of the model belong to edges of the lattice the boltzmann weights of the model obey the vertex type tetrahedron equation in the thermodynamic limit our model is equivalent to the bazhanov baxter model in the case whenn 2 we reproduce korepanov s and hietarinta s solutions of the tetrahedron equation as special cases

star triangle relations in the exactly solvable statistical models a regular method for analysis of lattice spin models with a nearest neighbour interaction is proposed star triangle relations in the form of functional equations are used parametric families of transfer matrices commuting due to star triangle relations are constructed the eigenvalues of transfer matrices as functions of the spectral parameter are shown to obey two functional equations the solution of these equations for the maximal eigenvalue yields the partition function of the model the method is applied for evaluation of the partition function of the critical potts models the ising model the ashkin teller model equivalent to the eight vertex model

an integrable 3d lattice model with positive boltzmann weights in this paper we construct a three dimensional 3d solvable lattice model with non negative boltzmann weights the spin variables in the model are assigned to edges of the 3d cubic lattice and run over an infinite number of discrete states the boltzmann weights satisfy the tetrahedron equation which is a 3d generalization of the yang baxter equation the weights depend on a free parameter 0 q 1 and three continuous field variables the layer to layer transfer matrices of the model form a two parameter commutative family this is the first example of a non trivial solvable 3d lattice model with non negative boltzmann weights

elastic plastic analysis of combined mode i ii and iii crack tip fields under small scale yielding conditions abstract within the context of the small strain approach combined mode i ii and iii near tip fields of stationary cracks in power law hardening materials are investigated we use a finite element technique to obtain asymptotic angular stress solutions for combined mode i and ii perturbed from mode iii these perturbation solutions with the same stress singularities as those of pure mode iii are presented for different hardening materials the perturbation results further suggest that the order of crack tip stress singularities varies smoothly with changing mode mixity we also employ full field finite element compulations to study the small scale yielding near tip fields for several combinations of prescribed remote mode i ii and iii elastic k fields these solutions verify an interesting pattern which agrees with the previous solutions for combined mode i and iii loading as well as those for combined mode ii and iii loading well within the plastic zone under near mode i mixed mode loadings the in plane stresses are slightly more singular than r t n 1 while the out of plane shear stresses are slightly less singular than r t n 1 where r is the radial distance to the lip and n is the strain hardening exponent of the material to explain the complex behavior of the near tip stresses we introduce an effective in plane shear stress and an effective out of plane shear stress to quantify the in plane and out of plane plastic shear at different orientations in a consistent manner the full field solutions also corroborate the observation that the singularities of the in plane slresses and the out of plane shear stresses vary smoothly with mode mixity

a sugeno integral inequality of carleman knopp type and some refinements abstract in this paper a carleman knopp type inequality for sugeno integrals is studied in a similar form than classical one considering all involved integrals in the sugeno sense with respect to the lebesgue measure also some refinements and examples are presented

baxter equations and the zamolodchikov model abstract a summary is given of the significance of the star triangle or yang baxter equations in the solution of two dimensional statistical mechanical models the extension to the three dimensional tetrahedron relations is quoted and it is shown how this can be used to obtain the partition function of the zamolodchikov model for an n lattice the n result differs from that recently obtained by bazhanov and stroganov

quantum 2 1 evolution model a quantum evolution model in 2 1 discrete spacetime connected with a 3d fundamental map is investigated map is derived as a map providing a zero curvature of a 2d linear lattice system called the current system in a special case of the local weyl algebra for dynamical variables the map appears to be canonical and it corresponds to the known operator valued matrix the current system is a type of the linear problem for the 2 1 evolution model a generating function for the integrals of motion for the evolution is derived with the help of the current system thus the complete integrability in 3d is proved directly

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

star triangle relation for a three dimensional model the solvablesl n chiral potts model can be interpreted as a three dimensional lattice model with local interactions to within a minor modification of the boundary conditions it is an ising type model on the body centered cubic lattice with two and three spin interactions the corresponding local boltzmann weights obey a number of simple relations including a restricted star triangle relation which is a modified version of the well known star triangle relation appearing in two dimensional models we show that these relations lead to remarkable symmetry properties of the boltzmann weight function of an elementary cube of the lattice related to the spatial symmetry group of the cubic lattice these symmetry properties allow one to prove the commutativity of the row to row transfer matrices bypassing the tetrahedron relation the partition function per site for the infinite lattice is calculated exactly

inequalities of holder and minkowski type for pseudo integrals with respect to interval valued measures abstract in the present paper the holder and minkowski type of inequality for the pseudo integral of a real valued function with respect to the interval valued pseudo additive measure is proven two cases of semirings are considered in the first case pseudo operations pseudo addition and pseudo multiplication are set by a strictly monotone continuous function in the second case the pseudo addition is the idempotent operation sup and pseudo multiplication is specified by a strictly monotone continuous function as in the first case trivial and nontrivial examples of interval valued pseudo additive measures are provided as well as holder and minkowski type of inequalities with respect to those measures

on a version of fuzzy jensen inequality based on the measure of level set abstract in this paper we present a sufficient condition for the continuity of distribution function f based on a condition of the measure of level sets from this result an estimate of jensen type inequality for sugeno integral is stated finally it is applied to establish jensen type estimates for several kinds of fuzzy numbers

thermodynamic limit for a spin lattice an integrable spin lattice is a higher dimensional generalization of integrable spin chains in this paper we consider a special spin lattice related to quantum mechanical interpretation of the three dimensional lattice model in statistical mechanics zamolodchikov and baxter the integrability means the existence of a set of mutually commuting operators expressed in the terms of local spin variables the significant difference between spin chain and spin lattice is that the commuting set for the latter is produced by a transfer matrix with two equitable spectral parameters there is a specific bilinear functional equation for the eigenvalues of this transfer matrix the spin lattice is investigated in this paper in the limit when both sizes of the lattice tend to infinity the limiting form of bilinear equation is derived it allows to analyze the distributions of eigenvalues of the whole commuting set the ground state distribution is obtained explicitly a structure of excited states is discussed

a spline based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations summary a novel enrichment function which can model arbitrarily shaped inclusions within the framework of the extended finite element method is proposed the internal boundary of an arbitrary shaped inclusion is first discretized and a numerical enrichment function is constructed on the fly using spline interpolation we consider a piecewise cubic spline which is constructed from seven localized discrete boundary points the enrichment function is then determined by solving numerically a nonlinear equation which determines the distance from any point to the spline curve parametric convergence studies are carried out to show the accuracy of this approach compared with pointwise and linear segmentation of points for the construction of the enrichment function in the case of simple inclusions and arbitrarily shaped inclusions in linear elasticity moreover the viability of this approach is illustrated on a neo hookean hyperelastic material with a hole undergoing large deformation in this case the enrichment is able to adapt to the deformation and effectively capture the correct response without remeshing copyright 2013 john wiley sons ltd

enriched element free galerkin methods for crack tip fields summary the element free galerkin efg method is a meshless method for solving partial di erential equations which uses only a set of nodal points and a cad like description of the body to formulate the discrete model it has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used an enriched efg formulation for fracture problems is proposed two methods are used 1 adding the asymptotic fields to the trial function and 2 augmenting the basis by the asymptotic fields a local mapping of the enriched fields for curved cracks is also described results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom 1997 by john wiley sons ltd

a contact algorithm for frictional crack propagation with the extended finite element method we present an incremental quasi static contact algorithm for path dependent frictional crack propagation in the framework of the extended finite element fe method the discrete formulation allows for the modeling of frictional contact independent of the fe mesh standard coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity the contact constraint is borrowed from non linear contact mechanics and embedded within a localized element by penalty method newton raphson iteration with consistent linearization is used to advance the solution we show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called latin for frictional crack propagation numerical examples include simulation of crack initiation and propagation in 2d plane strain with and without bulk plasticity in the presence of bulk plasticity the problem is also solved using an augmented lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution copyright 2008 john wiley sons ltd

a generalized finite element method for the simulation of three dimensional dynamic crack propagation this paper is aimed at presenting a partition of unity method for the simulation of three dimensional dynamic crack propagation the method is a variation of the partition of unity finite element method and hp cloud method in the context of crack simulation this method allows for modeling of arbitrary dynamic crack propagation without any remeshing of the domain in the proposed method the approximation spaces are constructed using a partition of unity pu and local enrichment functions the pu is provided by a combination of shepard and finite element partitions of unity this combination of pus allows the inclusion of arbitrary crack geometry in a model without any modification of the initial discretization it also avoids the problems associated with the integration of moving least squares or conventional shepard partitions of unity used in several meshless methods the local enrichment functions can be polynomials or customized functions these functions can efficiently approximate the singular fields around crack fronts the crack propagation is modeled by modifying the partition of unity along the crack surface and does not require continuous remeshings or mappings of solutions between consecutive meshes as the crack propagates in contrast with the boundary element method the proposed method can be applied to any class of problems solvable by the classical finite element method in addition the proposed method can be implemented into most finite element data bases several numerical examples demonstrating the main features and computational efficiency of the proposed method for dynamic crack propagation are presented

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

improved implementation and robustness study of the x fem for stress analysis around cracks numerical crack propagation schemes were augmented in an elegant manner by the x fem method the use of special tip enrichment functions as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh which is of industrial interest especially when a numerical model for crack propagation is desired this paper improves the implementation of the x fem method for stress analysis around cracks in three ways first the enrichment strategy is revisited the conventional approach uses a topological enrichment only the elements touching the front are enriched we suggest a geometrical enrichment in which a given domain size is enriched the improvements obtained with this enrichment are discussed second the conditioning of the x fem both for topological and geometrical enrichments is studied a preconditioner is introduced so that off the shelf iterative solver packages can be used and perform as well on x fem matrices as on standard fem matrices the preconditioner uses a local nodal cholesky based decomposition third the numerical integration scheme to build the x fem stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme a 2d benchmark problem is designed to show the improvements and the robustness

knot invariants associated with a particular n continuous limit of the baxter bazhanov model first we briefly recall the definition of the three dimensional baxter bazhanov lattice model the spins of this model are elements ofzn and ther matrix is associated to the algebrauqsl n ifq is a primitiventh root of unity then we construct a particularn limit of the model in which it is meaningful to interpret the spins as elements ofr and which gives the free gaussian boson model finally we study special limits of the rapidity variables in which we obtain braid group representations and we show that forn odd the associated knot invariants are given by the inverse of products of alexander polynomials evaluated at certain roots of unity

a jensen type inequality for fuzzy integrals in this paper we show a jensen type inequality for the sugeno integral we also discuss some conditions assuring the satisfaction of opposite inequality reverse jensen inequality

labelling schemes for tetrahedron equations and dualities between them zamolodchikov s tetrahedron equations which were derived by considering the scattering of straight strings can be written in three different labelling schemes one can use as labels the states of the vacua between the strings the states of the string segments or the states of the particles at the intersections of the strings we give a detailed derivation of the three corresponding tetrahedron equations and also show how the frenkel moore equations fits in as a non local string labelling we then discuss how an analogue of the wu kadanoff duality can be defined between each pair of the above three labelling schemes it turns out that there are two cases for which one can simultaneously construct a duality between all three pairs of labellings

some integral inequalities for fuzzy interval valued functions abstract this study presents new fuzzy versions of minkowski and beckenbach s integral inequalities without making use of the sugeno integral these new inequalities generalize the interval versions of the minkowski and beckenbach inequalities recently published and are obtained by introducing the p f a integrability concept for fuzzy interval valued functions by means of the kaleva integral and a fuzzy order relation this fuzzy order relation is defined level wise through the kulisch miranker order relation given on the interval space numerical examples that illustrate the applicability of the theory developed in this study are presented

tetrahedron equations and the relativistic s matrix of straight strings in 2 1 dimensions the quantums matrix theory of straight strings infinite one dimensional objects like straight domain walls in 2 1 dimensions is considered thes matrix is supposed to be purely elastic and factorized the tetrahedron equations which are the factorization conditions are investigated for the special two colour model the relativistic three strings matrix which apparently satisfies this tetrahedron equation is proposed

an enriched meshless method for non linear fracture mechanics this paper presents an enriched meshless method for fracture analysis of cracks in homogeneous isotropic non linear elastic two dimensional solids subject to mode i loading conditions the method involves an element free galerkin formulation and two new enriched basis functions types i and ii to capture the hutchinson rice rosengren singularity field in non linear fracture mechanics the type i enriched basis function can be viewed as a generalized enriched basis function which degenerates to the linear elastic basis function when the material hardening exponent is unity the type ii enriched basis function entails further improvements of the type i basis function by adding trigonometric functions four numerical examples are presented to illustrate the proposed method the boundary layer analysis indicates that the crack tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered whether for the near tip asymptotic field or for the far tip elastic field numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the j integral for the applied load intensities and material properties considered also the crack mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results furthermore the meshless results show excellent agreement with the experimental measurements indicating that the new basis functions are also capable of capturing elastic plastic deformations at a stress concentration effectively copyright 2003 john wiley sons ltd

corner transfer matrices of the chiral potts model ii the triangular lattice we consider a two dimensional edge interaction model satisfying the star triangle relations for the triangular lattice the corner transfer matrices are functions of three rapidities we show that they possess various factorization properties and satisfy certain equations we indicate how these equations can be solved for the ising model we then consider the three state chiral potts model and obtain low temperature solutions to the equations the conjectured formula for the order parameter the spontaneous magnetization is verified to one more order in a series expansion

the emerging role of number theory in exactly solvable models in lattice statistical mechanics abstract we review the baxter model the hard hexagon model and their multistate generalizations from a point of view that stresses the connection with modular functions and additive number theory it is shown for example that various physical quantities in the hard hexagon model are all expressible in terms of modular functions the use of rogers ramanujan type identities in solvable models is also reviewed

jensen and chebyshev inequalities for pseudo integrals of set valued functions set valued functions are an important mathematical notion and play a crucial role in several practical areas at the same time pseudo analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations this paper focuses on pseudo integration of set valued functions which is generalization of aumann s research and corresponding extensions of the jensen and chebyshev integral inequalities to the set valued case since the integral inequalities in question are widely used in various aspects of mathematics the main motivation for the presented research lies in the possibility of expanding the applicability of these inequalities by combining the properties of set valued functions with pseudo analysis

pseudo lp space and convergence in the framework of the pseudo analysis the classical l p space is generalized and there are proved important properties of introduced space three types of convergence of sequences of measurable functions are considered in this space the inequalities for integrals based on pseudo integral have been recently proposed as the holder minkowski and markov inequalities which are applied in observing relationship among introduced convergences

a two scale extended finite element method for modelling 3d crack growth with interfacial contact 3d fatigue crack growth problems are nowadays handled using x fem coupled with level set techniques it is also well established that such an approach allows mesh independent crack modelling and no remeshing during crack propagation however when contact and friction occur along the crack faces a discretization of the internal variables linked to the interface law is necessary the interface discretization is generally constructed from the finite elements cut by the crack as a consequence a mesh dependency between the bulk discretization and the interface discretization is introduced however the dimension of the possible non linearities arising at the crack interface like confined plasticity or unilateral contact with friction may be several orders of magnitude finer than the crack size a finer discretization is thus required to accurately capture these non linearities the aim of the present paper is to develop a method considering the 3d cracked structure and the crack interface as two independent global and local problems characterized by different length scales and different behaviors here the interface is seen as an autonomous entity with its own discretization variables and constitutive law a formulation involving three fields is used the interface is linked to the global problem in a weak sense in order to avoid instabilities in the contact solution two iterative strategies are considered to solve the contact problem two dimensional and three dimensional numerical examples are presented to demonstrate the ability of the model to solve the contact at the crack interface with or without propagation at a given level of accuracy

h continuity of fuzzy measures and set defuzzification the purpose of this work is to analyze the continuity of fuzzy measures with respect to the hausdorff metric on k r n the class of all nonempty compact subsets of r n as an application we study the continuity of set defuzzification processes on r n which are defined by aumann integral methods

is the zamolodchikov model critical evidence is presented in favour of the hypothesis that the zamolodchikov model an exactly solvable three dimensional lattice model without any temperature like parameters is critical the evidence is obtained by generalising the zamolodchikov model to include a temperature like variable the magnetisation curve of this model is then studied using a modified form of a variational approximation formulated earlier also the authors show the two layer zamolodchikov model corresponds to a critical free fermion model

berwald type inequality for sugeno integral abstract nonadditive measure is a generalization of additive probability measure sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure integral inequalities play important roles in classical probability and measure theory the classical berwald integral inequality is one of the famous inequalities this inequality turns out to have interesting applications in information theory in this paper berwald type inequality for the sugeno integral based on a concave function is studied several examples are given to illustrate the validity of this inequality finally a conclusion is drawn and a problem for further investigations is given

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

finite deformation formulation for embedded frictional crack with the extended finite element method we reformulate an extended finite element fe framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation including finite stretching and rotation for the fe representation we consider a galerkin approximation in which both the trial and weighting functions adapt to the current contact configuration contact and frictional constraints employ two kuhn tucker conditions a contact separation constraint nesting over a stick slip constraint for the case when the crack faces are in frictional sliding mode we integrate finite deformation bulk plasticity into the formulation using the multiplicative decomposition technique of nonlinear continuum mechanics we then present plane strain simulations demonstrating various aspects of the extended fe solutions the mechanisms considered include combined opening and frictional sliding in initially straight curved and s shaped cracks with and without bulk plasticity to gain further insight into the extended fe solutions we perform mesh convergence studies focusing on both the global and the local responses of structures with cracks including the distribution of the normal component of traction on the crack faces copyright 2009 john wiley sons ltd

zamolodchikov s tetrahedron equation and hidden structure of quantum groups the tetrahedron equation is a three dimensional generalization of the yang baxter equation its solutions define integrable three dimensional lattice models of statistical mechanics and quantum field theory their integrability is not related to the size of the lattice therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubic lattices obviously any such three dimensional model can be viewed as a two dimensional integrable model on a square lattice where the additional third dimension is treated as an internal degree of freedom therefore every solution of the tetrahedron equation provides an infinite sequence of integrable 2d models differing by the size of this hidden third dimension in this paper we construct a new solution of the tetrahedron equation which provides in this way the two dimensional solvable models related to finite dimensional highest weight representations for all quantum affine algebra where the rank n coincides with the size of the hidden dimension these models are related to an anisotropic deformation of the sl n invariant heisenberg magnets they were extensively studied for a long time but the hidden 3d structure was hitherto unknown our results lead to a remarkable exact rank size duality relation for the nested bethe ansatz solution for these models note also that the above solution of the tetrahedron equation arises in the quantization of the resonant three wave scattering model which is a well known integrable classical system in 2 1 dimensions

hermite hadamard type inequality for sugeno integrals abstract in this paper hermite hadamard type inequality for sugeno integrals based on m convex function is studied some examples are given to illustrate the results

rational mappings arborescent iterations and the symmetries of integrability we describe a class of nonlinear birational representations of groups generated by a finite number of involutions these groups are symmetries of the yang baxter equations and their higher dimensional generalizations they provide discrete dynamical systems with a variety of behaviors from chaotic to integrable according to the number of invariants of the representation

stabilized low order finite elements for frictional contact with the extended finite element method abstract contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity in which the normal contact pressure exhibits spurious oscillation this oscillation does not go away with mesh refinement and in some cases it even gets worse as the mesh is refined using a lagrange multipliers formulation we trace this problem to non satisfaction of the lbb condition associated with equal order interpolation of slip and normal component of traction in this paper we employ a stabilized finite element formulation based on the polynomial pressure projection ppp technique which was used successfully for stokes equation and for coupled solid deformation fluid diffusion using low order mixed finite elements for the frictional contact problem the polynomial pressure projection approach is applied to the normal contact pressure in the framework of the extended finite element method we use low order linear triangular elements tetrahedral elements for 3d for both slip and normal pressure degrees of freedom and show the efficacy of the stabilized formulation on a variety of plane strain plane stress and three dimensional problems

fatou s lemma for sugeno integral abstract fatou s lemma plays an important role in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which have been built on non additive measure in this paper a fatou type lemma for sugeno integral is shown the studied inequality is based on the classical fatou lemma for lebesgue integral to illustrate the proposed inequalities some examples are given

some constant solutions to zamolodchikov s tetrahedron equations the author presents constant solutions to the tetrahedron equations proposed by zamolodchikov 1981 in general from a given solution of the yang baxter equation there are two ways to construct solutions to the tetrahedron equation there are also other kinds of solutions they present some two dimensional solutions that were obtained by directly solving the equations using either an upper triangular or zamolodchikov s ansatz

let s baxterise we recall the concept of baxterisation of an r matrix or of a monodromy matrix which corresponds to build from one point in the r matrix parameter space the algebraic variety where the spectral parameter s live we show that the baxterisation which amounts to studying the iteration of a birational transformation is a win win strategy it enables to discard efficiently the non integrable situations focusing directly on the two interesting cases where the algebraic varieties are of the so called general type finite order iteration or are abelian varieties infinite order iteration we emphasize the heuristic example of the sixteen vertex model and provide a complete description of the finite order iterations situations for the baxter model we show that the baxterisation procedure can be introduced in much larger frameworks where the existence of some underlying yang baxter structure is not used we baxterise l operators local quantum lax matrices and quantum hamiltonians

necessary versus sufficient conditions for exact solubility of statistical models on lattices it is shown that under rather mild conditions the triangle relation represents a necessary condition for the existence of commuting transfer matrices of arbitrary size the cases of spin models and vertex models are treated separately

three dimensional vertex model in statistical mechanics from baxter bazhanov model we find that the boltzmann weight of the three dimensional baxter bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the wu kadanoff wegner duality between the cube and vertex type tetrahedron equations is obtained explicitly for the baxter bazhanov model then a three dimensional vertex model is obtained by considering the symmetry property of the weight function which corresponds to the three dimensional baxter bazhanov model the vertex type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube we write down the symmetry relations of the weight functions under the actions of the symmetry groupg of the cube the six angles with a constraint condition appearing in the tetrahedron equation can be regarded as the six spectra connected with the six spaces in which the vertextype tetrahedron equation is defined

tetrahedron equation and generalized quantum groups we construct families of solutions of the yang baxter equation from n products of three dimensional r and l operators satisfying the tetrahedron equation they are identified with the quantum r matrices for the hopf algebras known as generalized quantum groups depending on the number of r s and l s involved in the product the trace construction interpolates the symmetric tensor representations of and the antisymmetric tensor representations of whereas a boundary vector construction interpolates the q oscillator representation of and the spin representation of the intermediate cases are associated with an affinization of quantum superalgebras

generalization of the lyapunov type inequality for pseudo integrals we prove two kinds of lyapunov type inequalities for pseudo integrals one discusses pseudo integrals where pseudo operations are given by a monotone and continuous function g the other one focuses on the pseudo integrals based on a semiring 0 1 sup where the pseudo multiplication is generated some examples are given to illustrate the validity of these inequalities

on solving the ising model functional relation without elliptic functions the exactly solvable n state chiral potts model differs from previous solvable lattice models in that its mathematics leads to hyperelliptic rather than ordinary elliptic functions it is still an open question whether these hyperelliptic functions provide a useful computational tool in particular it has recently been shown that the functional relation for the eigenvalues of the transfer matrix can be solved directly without introducing such functions when n 2 the model reduces to the ising model and this method provides a novel and straightforward way of solving the ising model in fact the method simplifies considerably here we present the resulting technique

new development in extended finite element modeling of large elasto plastic deformations this paper presents new achievements in the extended finite element modeling of large elasto plastic deformation in solid problems the computational technique is presented based on the extended finite element method x fem coupled with the lagrangian formulation in order to model arbitrary interfaces in large deformations in x fem the material interfaces are represented independently of element boundaries and the process is accomplished by partitioning the domain with some triangular sub elements whose gauss points are used for integration of the domain of elements the large elasto plastic deformation formulation is employed within the x fem framework to simulate the non linear behavior of materials the interface between two bodies is modeled by using the x fem technique and applying the heaviside and level set based enrichment functions finally several numerical examples are analyzed including arbitrary material interfaces to demonstrate the efficiency of the x fem technique in large plasticity deformations copyright 2008 john wiley sons ltd

the fuzzy integral for monotone functions abstract in this paper we give some optimal upper bounds for the sugeno s integral of monotone functions more precisely we show that if g 0 0 is a continuous and strictly monotone function then the fuzzy integral value p 0 a g d with respect to the lebesgue measure verifies the following sharp inequalities a g a p p for the increasing case and b g p p for the decreasing case moreover we show that under adequate conditions these optimal inequalities provides a powerful tool for solving fuzzy integrals also some examples and application are presented

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

lattice gases and exactly solvable models we detail the construction of a family of lattice gas automata based on a model of t hooft proceeding by use of symmetry principles to define first the kinematics of the model and then the dynamics a spurious conserved quantity appears we use it to effect a radical transformation of the model into one whose spacetime configurations are equivalent to the two dimensional states of an exactly solvable statistical mechanics model the symmetric eight vertex model with parameters restricted to a disorder variety we comment on the implications of this identification for the original lattice gas

a stable and optimally convergent latin cutfem algorithm for multiple unilateral contact problems in this paper we propose a novel unfitted finite element method for the simulation of multiple body contact the computational mesh is generated independently of the geometry of the interacting solids which can be arbitrarily complex the key novelty of the approach is the combination of elements of the cutfem technology namely the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty type regularisation of discrete operators and the latin hybrid mixed formulation of complex interface conditions furthermore the novel p1 p1 discretisation scheme that we propose for the unfitted latin solver is shown to be stable robust and optimally convergent with mesh refinement finally the paper introduces a high performance 3d level set cutfem framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries with more than two bodies interacting at a single point

new solvable lattice models in three dimensions in this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models the first is the zamolodchikov model which is the only nontrivial model on a three dimen sional lattice so far solved the second is the chiral potts model on the square lattice and its generalization associated with theu q sl n algebra which is of current interest due to its connections with high genus algebraic curves and with representations of quantum groups at roots of unity we show that this last sl n generalized chiral potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square lattice layers with ann valued n 2 spin at each site further in then 2 case this three dimen sional model reduces after a modification of the boundary conditions to the zamolodchikov model we mentioned above

general minkowski type inequalities for sugeno integrals minkowski type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the pseudo additive operation

a mixed augmented lagrangian extended finite element method for modelling elastic plastic fatigue crack growth with unilateral contact the complete modelling of fatigue crack growth is still an industrial challenging issue for numerical methods a new technique for the finite element modelling of elastic plastic fatigue crack growth with unilateral contact on the crack faces is presented the extended finite element method x fem is used to discretize the equations allowing for the modelling of arbitrary cracks whose geometries are independent of the finite element mesh this paper presents an augmented lagrangian formulation in the x fem framework that is able to deal with elastic plastic crack growth with treatment of contact an original formulation which takes advantages of two powerful numerical methods is presented next the numerical issues such as contact treatment and numerical integration are addressed and finally numerical examples are shown to validate the method copyright 2007 john wiley sons ltd