migrative uninorms and nullnorms over t norms and t conorms in this paper the notions of migrative uninorms and nullnorms over a fixed t norm t and over a fixed t conorm s are introduced and studied all cases when the uninorm u lies in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations of u and t and for all possible combinations of u and s a similar study is done for nullnorms

a recursive approach to local mesh refinement in two and three dimensions abstract the newest vertex strategy for local refinement in two dimensions is reviewed and discussed a recursive algorithm for local refinement of tetrahedral meshes in three dimensions based on similar bisection strategy is described the recursive approach requires certain restrictions on the initial mesh on the other hand under this condition the refinement process can be kept as local as needed and it can be fully inverted simple data structures and derefinement algorithms are also outlined

an element free galerkin approach for rigidflexible coupling dynamics in 2d state based on an improved element free galerkin efg method and the geometric nonlinear elastic theory an element free numerical approach for rigidflexible coupling dynamics of a rotating hubbeam system is implemented using the hamilton principle the coupled nonlinear integral differential governing equations are derived in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement by the efg method where the global interpolating moving least squares imls and generalized moving least squares igmls were used for discretizing the longitudinal and transverse deformation variables respectively the spatially element free discretized dynamic equations of the system are obtained and the newmark scheme was selected as the time integration method for the numerical computation the superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions the transverse bending vibration and structural dynamics of the flexible beam in non inertial system are analyzed in the numerical simulations and influence parameters of the efg method are also fully discussed simulation results verify the feasibility of the improved efg approach for rigidflexible coupling dynamics

a family of strict and discontinuous triangular norms answers to some questions about triangular norms are given precisely a procedure of construction of infinitely many triangular norms is obtained one for each operation n2 n such that n is a strictly ordered commutative semigroup each of them is discontinuous at each point of a dense subset of 0 1 2 and it satisfies the condition t kx y t x ky for infinitely many k 0 1

migrative t norms with respect to continuous ordinal sums abstract in this paper we study and characterize continuous migrative t norms t with respect to a continuous t norm t0 depending on whether is an idempotent element of t0 or not the t0 migrative property restricts the ordinal sum structure of t especially locally i e at or around it outside this well defined neighbourhood of the t norm t can be arbitrary under the only condition of keeping it continuous the investigation exploits the ordinal sum structure of continuous t norms and our former results related to the migrative property

on the migrativity of triangular subnorms the a t migrative triangular subnorms where t stands for the three prototype triangular norms namely the product the lukasiewicz t norm and the minimum are investigated in detail the paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous additive generator is a t migrative with respect to any of the three prototype triangular norms

migrativity property for uninorms the migrative uninorms over a fixed uninorm with different neutral elements are presented all cases when both uninorms lay in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations the solutions obtained generalize the results where both uninorms have the same neutral elements

on continuous triangular norms that are migrative in this paper we completely describe all continuous migrative triangular norms since the migrative property excludes both idempotent and nilpotent classes the characterization and construction is carried out by solving a functional equation for additive generators of strict t norms we also study cases when the construction results in a smooth generator

the migrativity equation for uninorms revisited abstract the migrativity equation with interesting applications in decision making and image processing has been extensively discussed involving different kinds of aggregation functions from t norms and t conorms to uninorms nullnorms and some generalizations of them in recent papers the already known results concerning the migrativity of two uninorms are based on the assumption that both uninorms belong to one of the most studied classes of uninorms in this paper we will explore the migrativity equation involving uninorms in a most general setting specifically we will study the migrativity between two uninorms in the cases when the second uninorm lies in any of the most studied classes of uninorms but the first one is any uninorm with no further assumptions we will show along the paper that many new solutions appear from this new point of view that were not included in the previous approaches

a generalization of the migrativity property of aggregation functions this paper brings a generalization of the migrativity property of aggregation functions suggested in earlier work of some of the present authors by imposing the a migrativity property of durante and sarkoci for all values of a instead of a single one replacing the algebraic product by an arbitrary aggregation function b naturally leads to the properties of a b migrativity and b migrativity this generalization establishes a link between migrativity and a particular case of aczel s general associativity equation already considered by cutello and montero as a recursive formula for aggregation following a basic investigation emphasis is put on aggregation functions that can be represented in terms of an additive generator more specifically strict t norms strict t conorms and representable uninorms

the uniform saturation property for a singularly perturbed reaction diffusion equation although adaptive finite element methods for solving elliptic problems often work well in practice they are usually not proven to converge for poisson like problems an exception is given by the method of dorfler 8 that was later improved by morin nochetto and siebert 11 in this paper we extend these methods by constructing an adaptive finite element method for a singularly perturbed reaction diffusion equation that in energy norm converges uniformly in the size of the reaction term moreover in this algorithm the arising galerkin systems are solved only inexactly so that generally the number of arithmetic operations is equivalent to the number of triangles in the final partition

on migrativity property for uninorms recently u 0 migrative uninorms u were introduced and discussed where u and u 0 are two uninorms with neutral element e in this paper we will further study u 2 migrative uninorms u 1 where u 1 and u 2 are two uninorms with different neutral elements e 1 and e 2 respectively all cases when the uninorm u 1 and u 2 are in different families out of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations of u 1 and u 2

convergence and quasi optimality of an adaptive finite element method for controlling l 2 errors in this paper a contraction property is proved for an adaptive finite element method for controlling the global l 2 error on convex polyhedral domains furthermore it is shown that the method converges in l 2 with the best possible rate the method that is analyzed is the standard adaptive method except that if necessary additional refinements are made to keep the meshes sufficiently mildly graded this modification does not compromise the quasi optimality of the resulting algorithm

adaptive finite element frequency domain method for eddy current problems in the present paper adaptive finite element methods are studied for time harmonic eddy current problems in the case of three dimensional isotropic and linear materials we adopt the formulation based on the magnetic field and a magnetic scalar potential in this paper since it needs the least number of unknowns reliable and efficient a posteriori error estimates are obtained and the efficiency of the adaptive algorithm is demonstrated by numerical and engineering experiments

signatures definitions operators and applications to fuzzy modelling this paper presents a new framework for the symbolic representation of data which is referred to as signatures the definitions of signatures and of signature trees are first given original operators on signatures are next presented i e contraction extension pruning addition multiplication and grafting attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed an example is included to accompany the theoretical results

migrative uninorms and nullnorms over t norms and t conorms revisited abstract in 2015 mas et al investigated the migrativity of uninorms and nullnorms over any fixed t norm and t conorm first they introduced the concept of migrative uninorm over any fixed t norm in addition they showed equivalent characterizations of the migrativity equation when the uninorm belongs to one certain class e g u min u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 and then they gave the notion of migrative uninorms over any fixed t conorm and proposed the migrativity equation using an analogous method finally they discussed the migrativity of nullnorms over any fixed t norm and t conorm and obtained equivalent characterizations of the related migrativity equations respectively however they did not discuss the migrativity property of a conjunctive resp disjunctive uninorm non locally internal on the boundary over any fixed t norm resp t conorm and the migrativity property of a conjunctive resp disjunctive uninorm locally internal on the boundary over any continuous t norm resp t conorm to fill the gap in this paper we explore some new results on the migrativity property of a conjunctive resp disjunctive uninorm over any fixed t norm resp t conorm and give some new characterizations of the migrativity property of nullnorms over any fixed t norm and t conorm respectively

an adaptive uzawa fem for the stokes problem convergence without the inf sup condition we introduce and study an adaptive finite element method fem for the stokes system based on an uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity we show linear convergence in terms of the outer iteration counter for the pairs of spaces consisting of continuous finite elements of degree k for velocity whereas for pressure the elements can be either discontinuous of degree k 1 or continuous of degree k 1 and k the popular taylor hood family is the sole example of stable elements included in the theory which in turn relies on the stability of the continuous problem and thus makes no use of the discrete inf sup condition we discuss the realization and complexity of the elliptic adaptive inner solver and provide consistent computational evidence that the resulting meshes are quasi optimal

supermigrativity of aggregation functions abstract a functional inequality called supermigrativity was recently introduced for bivariate semi copulas and applied in various problems arising in the study of aging properties of stochastic systems here we revisit this notion and extend it to the case of aggregation functions in higher dimensions in particular we show how supermigrativity can be expressed via monotonicity of a function with respect to logarithmic majorization ordering of real vectors various alternative characterizations of supermigrativity are illustrated together with some of its weaker versions several examples show similarities and differences between the bivariate and the general case

convex combinations of uninorms and triangular subnorms abstract the problem whether a non trivial convex combination of two continuous triangular norms can be a t norm was extensively studied in the last decades bringing the negative answer in all examined special cases on the other hand in the field of non continuous t norms including left continuous t norms several examples were found including mainly a convex combination of an migrative t norm and the drastic product t norm or a convex combination of ordinal sums of product related t subnorms recently convex combinations of uninorms were discussed in 18 since any uninorm with the neutral element e 0 1 restricted to 0 e 2 is isomorphic to a t norm this investigation extends the original problem of a convex combination of t norms given by alsina frank and schweizer in this work we will study convex combinations of uninorms further covering uninorms with continuous underlying functions uninorms with different neutral elements and representable uninorms we will also show that convex combinations of triangular subnorms play a major role in this investigation

generalizing the migrativity of continuous t norms this paper generalizes the migrativity of triangular norms t norms for short precisely we find those continuous t norms t which satisfy t l 1x l 2y email protected 3t x y where l email protected 0 1 i 1 2 3 are given it is worth pointing out that this paper provides a new characterization of the product t norm

supermigrative semi copulas and triangular norms a semi copula s 0 1 2 0 1 is called supermigrative if it is commutative and satisfies s ax y s x ay for all email protected 0 1 and for all x email protected 0 1 such that y

migrativity equation for uninorms with continuous underlying operators abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theorem as a kind of restricted general associative equation the migrativity equation has been proven to be useful in a wide range of fields like decision making aggregation of information image processing and so on in the literature the already existing results concerning the migrativity equation for two uninorms are based on the assumption that one of the uninorms belongs to one of the most studied classes of uninorms or that they have the same neutral element in this study we will explore the migrativity equation involving uninorms in a most general setting to be specific we investigate the migrativity between two uninorms with only continuous underlying operators then many new solutions of the equation are fully characterized from this new point of view

a posteriori error estimator and error control for contact problems in this paper we consider two error estimators for one body contact problems the first error estimator is defined in terms of h div conforming stress approximations and equilibrated fluxes while the second is a standard edge based residual error estimator without any modification with respect to the contact we show reliability and efficiency for both estimators more over the error is bounded by the first estimator with a constant one plus a higher order data oscillation term plus a term arising from the contact that is shown numerically to be of higher order the second estimator is used in a control based afem refinement strategy and the decay of the error in the energy is shown several numerical tests demonstrate the performance of both estimators

bimigrativity of binary aggregation functions we introduce the notions of bimigrativity and total bimigrativity of an aggregation function w r t another aggregation function as a natural generalization of the notions of migrativity and bisymmetry we investigate the role of the presence of neutral or absorbing elements we also pay attention to the class of weighted quasi arithmetic means a well known class of bisymmetric aggregation functions

an extension of the migrative property for uninorms in this paper the notion of a migrative uninorms over a fixed uninorm u 0 with the same neutral element is introduced all uninorms u that are a migrative over a uninorm u 0 are studied all cases when u and u 0 have continuous underlying operations and belong to any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations

on the α migrativity of semicopulas quasi copulas and copulas in this paper we address the problem of a migrativity for a fixed a for semicopulas copulas and quasi copulas we introduce the concept of an a sum of semicopulas this new concept allows us to completely characterize a migrative semicopulas and copulas moreover a sums also provide a means to obtain a partial characterization of a migrative quasi copulas

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

aggregation of convex intuitionistic fuzzy sets aggregation of intuitionistic fuzzy sets is studied from the point of view of preserving various kinds of convexity we focus on aggregation functions for intuitionistic fuzzy sets these functions correspond to simultaneous separate aggregations of the membership as well as of the nonmembership indicators it is performed by means of the so called representable functions sufficient and necessary conditions are analyzed in order to guarantee that the composition of two intuitionistic fuzzy sets preserves convexity

on α β homogeneous copulas we introduce and characterize the family of a b homogeneous copulas and study some of its salient properties such as the greatest and the lowest copulas measures of association and the relationships with the a migrativity and invariant copulas

on the α migrativity of multivariate semi copulas in this paper we introduce and study the a migrative property for the class of multivariate semi copulas in particular a characterization of a migrative copulas is provided

migrativity property for uninorms and semi t operators in this paper the notions of migrative uninorms over semi t operators and migrative semi t operators over uninorms are introduced and investigated all solutions of the migrativity equations for all possible combinations of semi t operators and uninorms are characterized

residual error estimate for bem based fem on polygonal meshes a conforming finite element method on polygonal meshes is reviewed which handles hanging nodes naturally trial functions are defined to fulfil the homogeneous pde locally and they are treated by means of local boundary integral equations using a quasi interpolation operator of clement type a residual based error estimate is obtained this a posteriori estimator can be used to rate the accuracy of the approximation over polygonal elements or it can be applied to an adaptive bem based fem the numerical experiments confirm our results and show optimal convergence for the adaptive strategy on general meshes

convergence of simple adaptive galerkin schemes based on h h 2 error estimators we discuss several adaptive mesh refinement strategies based on h h 2 error estimation this class of adaptive methods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead we prove that under the saturation assumption these adaptive algorithms are convergent our framework applies not only to finite element methods but also yields a first convergence proof for adaptive boundary element schemes for a finite element model problem we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

some results of weighted quasi arithmetic mean of continuous triangular norms the weighted quasi arithmetic mean of continuous triangular norms is investigated some results on convex combination of continuous triangular norms in ouyang and fang y ouyang j x fang some observations about the convex combination of continuous triangular norms nonlinear anal tma 68 2008 3382 3387 are generalized several open problems are posed

a note on the convex combinations of triangular norms we consider a property on binary operations which we call a migrativity and we use it to obtain t norms by means of convex combinations of two t norms one of them being discontinuous

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

opacity and entanglement of polymer chains we argue that the mean crossing number of a random polymer configuration is simply a measure of opacity without being closely related to entanglement as claimed by several authors we present an easy way of estimating its asymptotic behaviour numerically these estimates agree for random walks theta polymers for self avoiding walks and for compact globules with analytic estimates giving log n a b n 2 1 and n 1 3 respectively for the average number of crossings per monomer in the limit n while the result for compact globules agrees with a rigorous previous estimate the result for self avoiding random walks disagrees with previous numerical estimates

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

some new results on the migrativity of uninorms over overlap and grouping functions abstract in 2018 qiao and hu 48 studied the migrativity of uninorms over overlap and grouping functions when the uninorm u belongs to one certain class e g u min u max the family of idempotent uninorms representable uninorms or uninorms continuous on 0 1 2 in addition they obtained some equivalent characterizations of them this paper will continue to consider the characterizations of this kind of migrativity equations by means of the ordinal sum of overlap and grouping functions we give the necessary and sufficient conditions for the solutions of the o migrativity equation when the uninorm u becomes a t norm or a conjunctive uninorm locally internal on the boundary and the g migrativity equation when the uninorm u becomes a t conorm or a disjunctive uninorm locally internal on the boundary respectively

an extension of the migrative property for triangular norms in this paper we extend the migrative property of triangular norms by allowing an arbitrary fixed t norm t 0 in the defining equation instead of the originally used product equivalent forms of this extended migrativity are also provided and proved two particular cases when t 0 is either the minimum or the lukasiewicz t norm are studied in these cases all continuous extended migrative t norms are characterized and represented the proofs are constructive which helps the reader to build up various families of extended migrative t norms

adaptive wavelet methods for elliptic operator equations convergence rates this paper is concerned with the construction and analysis of wavelet based adaptive algorithms for the numerical solution of elliptic equations these algorithms approximate the solution u of the equation by a linear combination of n wavelets therefore a benchmark for their performance is provided by the rate of best approximation to u by an arbitrary linear combination of n wavelets so called n term approximation which would be obtained by keeping the n largest wavelet coefficients of the real solution which of course is unknown the main result of the paper is the construction of an adaptive scheme which produces an approximation to u with error o n s in the energy norm whenever such a rate is possible by n term approximation the range of s 0 for which this holds is only limited by the approximation properties of the wavelets together with their ability to compress the elliptic operator moreover it is shown that the number of arithmetic operations needed to compute the approximate solution stays proportional to n the adaptive algorithm applies to a wide class of elliptic problems and wavelet bases the analysis in this paper puts forward new techniques for treating elliptic problems as well as the linear systems of equations that arise from the wavelet discretization