a tensor artificial viscosity using a mimetic finite difference algorithm abstract we have developed a two dimensional tensor artificial viscosity for finite difference shock wave computations the discrete viscosity tensor is formed by multiplying the gradient of velocity tensor by a scalar term the scalar term is based on the form of viscosity first presented by kurapatanko and also contains a limiter designed to switch off the viscosity for shockless compression and rigid body rotation mimetic discretizations are used to derive the form of the momentum and energy equations for a nonorthogonal grid where the viscosity tensor is evaluated at the zone edges the advantage of the tensor viscosity is a reduction of the dependence of the solution on the relation of the grid to the flow structure

some kinds of view the fuzzy filters of bl algebras the concepts of view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras are introduced and some related properties are investigated some characterizations of these generalized fuzzy filters are derived in particular we describe the relationships among ordinary fuzzy implicative positive implicative and fantastic filters view the mathml source fuzzy implicative positive implicative and fantastic filters and view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras finally we prove that a fuzzy set f of a bl algebra l is an view the mathml source fuzzy implicative filter of l if and only if it is both an view the mathml source fuzzy positive implicative filter and an view the mathml source fuzzy fantastic filter

the mimetic finite difference method for the 3d magnetostatic field problems on polyhedral meshes we extend the mimetic finite difference mfd method to the numerical treatment of magnetostatic fields problems in mixed div curl form for the divergence free magnetic vector potential to accomplish this task we introduce three sets of degrees of freedom that are attached to the vertices the edges and the faces of the mesh and two discrete operators mimicking the curl and the gradient operator of the differential setting then we present the construction of two suitable quadrature rules for the numerical discretization of the domain integrals of the div curl variational formulation of the magnetostatic equations this construction is based on an algebraic consistency condition that generalizes the usual construction of the inner products of the mfd method we also discuss the linear algebraic form of the resulting mfd scheme its practical implementation and discuss existence and uniqueness of the numerical solution by generalizing the concept of logically rectangular or cubic meshes by hyman and shashkov to the case of unstructured polyhedral meshes the accuracy of the method is illustrated by solving numerically a set of academic problems and a realistic engineering problem

fuzzy filters of bl algebras the aim of this paper is to introduce the notions of fuzzy filters fuzzy prime filters and the cosets of a fuzzy filter in bl algebras and investigate some of their properties the fuzzy filter generated by a fuzzy set is discussed some characterizations of fuzzy filters and fuzzy prime filters are derived the extension theorem of fuzzy prime filters and the fuzzy prime filters theorem are established finally we prove that the algebra l f which is the set of all cosets of f is a bl algebra and is isomorphic to the bl algebra l ff 1 where ff 1 x l f x f 1 moreover each bl algebra l is a subdirect product of linearly ordered bl algebras l fi i where fi i are fuzzy prime filters of l

convergence analysis of the mimetic finite difference method for elliptic problems we propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes the a priori error analysis relies on the connection between the mimetic formulation and the lowest order raviart thomas mixed finite element method the theoretical results are confirmed by numerical experiments

new types of fuzzy filters of bl algebras this paper introduces the concepts of a b fuzzy implicative positive implicative fantastic filters and b a fuzzy implicative positive implicative fantastic filters of bl algebras where a b c q d c q d c q d a b c q d c q d c q d a c q d and b c q d and some related properties are investigated special attention is paid to c c q d fuzzy implicative positive implicative fantastic filters and c c q d fuzzy implicative positive implicative fantastic filters which are generalizations of q fuzzy implicative positive implicative fantastic filters and q fuzzy implicative positive implicative fantastic filters studied in ma et al 2008 2009 34 35 it also points out that examples 3 1 2 3 1 9 3 2 2 3 2 9 and 3 3 9 in ma et al 2009 35 are incorrect

fuzzy boolean and positive implicative filters of bl algebras the aim of this paper is to introduce the notions of fuzzy boolean filters and fuzzy positive implicative filters in bl algebras and to investigate their properties several characterizations of fuzzy boolean filters and fuzzy positive implicative filters are derived the extension theorems of fuzzy boolean filters and fuzzy positive implicative filters are obtained the relation between fuzzy boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy boolean filter is a fuzzy positive implicative filter but the converse may not be true furthermore the conditions under which a fuzzy positive implicative filter is a fuzzy boolean filter are established

optimal control of evolutionary quasi newtonian fluids we are interested in the necessary optimality conditions for optimal control problems of systems describing the unsteady flow of incompressible shear thickening fluids to overcome the difficulties related to the differentiability of the control to state mapping consequence of the lack of regularity of the state variable we first establish some intermediate optimality conditions and then pass to the limit

convergence analysis of the high order mimetic finite difference method we prove second order convergence of the conservative variable and its flux in the high order mfd method the convergence results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients for the case of non constant coefficients we also develop a new family of high order mfd methods theoretical result are confirmed through numerical experiments

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

fuzzy h v ideals in γ h v rings in this paper by means of a kind of new idea we consider the q fuzzy h v ideals of a c h v ring the concept of c h v rings which is a generalization of c rings and h v rings is introduced the notion of q fuzzy h v ideals of a c h v ring is provided and some related properties are investigated the concept of implication based fuzzy h v ideals of a c h v ring is studied in particular the implication operators in the lukasiewicz system of continuous valued logic are discussed finally the homomorphism of q fuzzy h v ideals of a c h v ring is explored

boolean products of bl algebras the representation of algebras by boolean products is a very general problem in universal algebra in this paper we shall characterize the boolean products of bl chains the weak boolean products of local bl algebras and the weak boolean products of perfect bl algebras

e e v q fuzzy normal quasinormal and maximal subgroups abstract the notions of and q fuzzy normality and quasinormality for a q fuzzy subgroup are introduced the notions of an q fuzzy core subgroup and an q fuzzy p sylow subgroup are also introduced and some fundamental properties are dealt with q fuzzy normality and q fuzzy quasinormality are found to be more generalised concepts than those introduced by others a detailed study with a fuzzy maximal subgroup is incorporated with the limitation of this concept

a framework for developing a mimetic tensor artificial viscosity for lagrangian hydrocodes on arbitrary polygonal meshes we construct a new mimetic tensor artificial viscosity on general polygonal meshes the tensor artificial viscosity is based on discretization of coordinate invariant operators divergence of a tensor and gradient of a vector the focus of this paper is on the non symmetric form div email protected u of the tensor artificial viscosity the discretizations of this operator is derived for the case of a full tensor coefficient m however in the numerical experiments we only use scalar m we prove that the new tensor viscosity preserves spatial symmetry on special meshes we demonstrate performance of the new viscosity for the noh implosion sedov explosion and saltzman piston problems on a set of various polygonal meshes in both cartesian and axisymmetric coordinate systems

a new view of fuzzy hypernear rings in this survey article we first introduce the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set this concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we consider the interval valued q fuzzy sub hypernear rings hyperideals of a hypernear ring and hence a generalization of a fuzzy sub near ring ideal is given some related properties of fuzzy hypernear rings are described finally we consider the concept of implication based interval valued fuzzy sub hypernear rings hyperideals in a hypernear ring in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

virtual element methods for plate bending problems abstract we discuss the application of virtual elements to linear plate bending problems in the kirchhoff love formulation as we shall see in the virtual element environment the treatment of the c 1 continuity condition is much easier than for traditional finite elements the main difference consists in the fact that traditional finite elements for every element k and for every given set of degrees of freedom require the use of a space of polynomials or piecewise polynomials for composite elements for which the given set of degrees of freedom is unisolvent for virtual elements instead we only need unisolvence for a space of smooth functions that contains a subset made of polynomials whose degree determines the accuracy as we shall see the non polynomial part of our local spaces does not need to be known in detail and therefore the construction of the local stiffness matrix is simple and can be done for much more general geometries

on the logic foundation of fuzzy reasoning abstract fuzzy reasoning and fuzzy formal deduction theory are two closely related subjects and each of them has been investigated by many researchers unfortunately it seems that the two branches have not been successfully connected the aim of this paper is to establish a so called quasi propositional deductive system syntactically as well as semantically and then set a logic foundation for developing the theory of fuzzy reasoning therefrom

generalizations of fuzzy subalgebras in bck bci algebras more general form of the notion of quasi coincidence of a fuzzy point with a fuzzy set is considered and generalizations of results in the papers y b jun on a b fuzzy subalgebras of bck bci algebras bull korean math soc 42 4 2005 703 711 y b jun fuzzy subalgebras of type a b in bck bci algebras kyungpook math j 47 2007 403 410 are discussed the notions of q k fuzzy subalgebras and email protected q k fuzzy subalgebras in a bck bci algebra x are introduced and several properties are investigated characterizations of email protected q k fuzzy subalgebra in a bck bci algebra x are discussed

the finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes we construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving discrete extremum principle and positivity on various distorted meshes

some types of generalized fuzzy filters of bl algebras the aim of this paper is to introduce the notions of interval valued q fuzzy boolean implicative positive implicative and fantastic filters in bl algebras and to investigate some related properties some characterizations of these generalized fuzzy filters are derived finally the relations among these generalized fuzzy filters are discussed it is proved that an interval valued q fuzzy filter in bl algebras is an interval valued q fuzzy boolean implicative filter if and only if it is both an interval valued q fuzzy positive implicative filter and an interval valued q fuzzy fantastic filter

generalized fuzzy h bi ideals and h quasi ideals of hemirings a new kind of generalized fuzzy h ideals of a hemiring namely the set membership variant set membership variantlogical orq fuzzy h bi ideal resp h quasi ideal is studied and the relationships between these generalized fuzzy h ideals are described some characterization theorems of prime and semiprime set membership variant set membership variantlogical orq fuzzy h bi ideals resp h quasi ideals of a hemiring are also given in particular we show that the h hemiregular hemirings and h intra hemiregular hemirings can be described by using some of their generalized fuzzy h ideals finally the implication based fuzzy h bi ideals resp h quasi ideals of a hemiring are considered

characterizations of hemirings by νq k fuzzy ideals in this paper we define q k fuzzy h sub hemirings q k fuzzy h bi ideals q k fuzzy h quasi ideals we characterize h hemiregular and h intra hemiregular hemirings by the properties of their q k fuzzy h ideals q k fuzzy h bi idealsand q k fuzzy h quasi ideals some of these characterizations are generalizations of the characterizations given in 36 x ma j zhan generalized fuzzyh bi ideals and h quasi ideals of hemirings inform sci 179 2009 1249 1268

optimal control for an adsorbate induced phase transition model this paper is concerned with the optimal control problem for an adsorbate induced phase transition model that is we show the existence of the optimal control and derive the optimality conditions by showing the differentiability of the cost functional with respect to the control

optimality conditions for distributed control problems with nonlinear state equation we develop an abstract approximating process for control problems with convex cost governed by evolution equations involving monotone operators applications are given concerning necessary conditions of optimality for distributed control problems with hyperbolic parabolic and delay differential state systems these conditions are expressed by means of the clarke 11 generalized gradient

redefined fuzzy hv submodules and many valued implications this paper considers a relationship between fuzzy sets and algebraic hyperstructures a generalization of ideas presented by davvaz b davvaz fuzzy h v submodules fuzzy sets syst 117 2001 477 484 and bhakat and das s k bhakat p das email protected q fuzzy subgroup fuzzy sets syst 80 1996 359 368 is presented in fact the main purpose of this paper is to introduce and study a new sort of fuzzy h v submodule of an h v module called email protected q fuzzy h v submodules these fuzzy h v submodules are characterized by their level h v submodules the concept of a fuzzy h v submodule with thresholds is introduced and some interesting properties are investigated

convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes the stability and convergence properties of the mimetic finite difference method for diffusion type problems on polyhedral meshes are analyzed the optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved

on filter theory of residuated lattices the aim of this paper is to develop the filter theory of general residuated lattices first we extend some particular types of filters and fuzzy filters in bl algebras and mtl algebras naturally to general residuated lattices and further enumerate some relative results obtained in bl algebras or mtl algebras which still hold in general residuated lattices next we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices which are two new types of filters and fuzzy filters and derive some of their characterizations finally we discuss the relations between fuzzy regular filters and several other special fuzzy filters and also characterize some special classes of residuated lattices by filters or fuzzy filters

new types of fuzzy ideals in bck bci algebras a generalization of an email protected q fuzzy ideal of a bck bci algebra is discussed characterizations of an email protected q k fuzzy ideal and an email protected email protected email protected q email protected fuzzy ideal are provided conditions for an email protected q k fuzzy ideal resp email protected email protected email protected q email protected fuzzy ideal to be a fuzzy ideal are provided using the notion of a fuzzy ideal with thresholds characterizations of a fuzzy ideal an email protected q k fuzzy ideal and an email protected email protected email protected q email protected fuzzy ideal are discussed

α β fuzzy ideals of hemirings we give a characterization of different types of a b fuzzy ideals of hemirings where a b q q q and a q special attention is paid to q fuzzy prime and semiprime ideals

error analysis for a mimetic discretization of the steady stokes problem on polyhedral meshes we present the development convergence analysis and numerical tests of the mimetic finite difference method for the stokes problem on two dimensional polygonal and three dimensional polyhedral meshes

an improved monotone finite volume scheme for diffusion equation on polygonal meshes we construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes the new scheme uses the cell edge unknowns instead of cell vertex unknowns as the auxiliary unknowns in order to improve the accuracy of monotone scheme our scheme is locally conservative and has only cell centered unknowns numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes specially numerical results show that the new scheme is robust and more accurate than the existing monotone scheme on some kinds of meshes

first and second order optimality conditions for a class of optimal control problems with quasilinear elliptic equations a class of optimal control problems for quasilinear elliptic equations is considered where the coefficients of the elliptic differential operator depend on the state function first and second order optimality conditions are discussed for an associated control constrained optimal control problem main emphasis is laid on second order sufficient optimality conditions to this aim the regularity of the solutions to the state equation and its linearization is studied in detail and the pontryagin maximum principle is derived one of the main difficulties is the nonmonotone character of the state equation

high order mimetic finite difference method for diffusion problems on polygonal meshes the mimetic finite difference mfd methods mimic important properties of physical and mathematical models as a result conservation laws solution symmetries and the fundamental identities of the vector and tensor calculus are held for discrete models the mfd methods retain these attractive properties for full tensor coefficients and arbitrary polygonal meshes which may include non convex and degenerate elements the existing mfd methods for solving diffusion type problems are second order accurate for the conservative variable temperature pressure energy etc and only first order accurate for its flux we developed new high order mfd methods which are second order accurate for both scalar and vector variables the second order convergence rates are demonstrated with a few numerical examples on randomly perturbed quadrilateral and polygonal meshes

semigroups characterized by c c νqk fuzzy ideals generalizing the notions of q fuzzy ideal q fuzzy quasi ideal and q fuzzy bi ideal the concepts of q k fuzzy ideal q k fuzzy quasi ideal and q k fuzzy bi ideal are defined different classes of semigroups are characterized by the properties of these fuzzy ideals

a higher order formulation of the mimetic finite difference method a new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes this approach provides a higher order accurate approximation to the flux of the exact solution in analogy with the original formulation a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability the scalar solution field is approximated by a piecewise constant function a computationally efficient postprocessing technique is also proposed to get a piecewise quadratic polynomial approximation to the exact scalar variable finally optimal convergence rates and accuracy improvement with respect to the lower order formulation are shown by numerical examples

convergence of the mimetic finite difference method for eigenvalue problems in mixed form optimal convergence rates for the mimetic finite difference method applied to eigenvalue problems in mixed form are proved the analysis is based on a new a priori error bound for the source problem and relies on the existence of an appropriate elemental lifting of the mimetic discrete solution compared to the original convergence analysis of the method the new a priori estimate does not require any extra regularity assumption on the right hand side of the source problem numerical results confirming the optimal behavior of the method are presented

a new discretization methodology for diffusion problems on generalized polyhedral meshes we develop a family of inexpensive discretization schemes for diffusion problems on generalized polyhedral meshes with elements having non planar faces the material properties are described by a full tensor we also prove superconvergence for the scalar pressure variable under very general assumptions the theoretical results are confirmed with numerical experiments in the practically important case of logically cubic meshes with randomly perturbed nodes the mixed finite element with the lowest order raviart thomas elements does not converge while the proposed mimetic method has the optimal convergence rate 2007 elsevier b v all rights reserved

generalized fuzzy hyperideals of hyperrings the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set is considered in fact this is a generalized concept of the quasi coincidence of a fuzzy point with a fuzzy set by using this new idea the notion of interval valued a b fuzzy hyperideals in a hyperring is introduced and consequently a generalization of a fuzzy hyperideal is defined in this paper we study the related properties of the fuzzy hyperideals and in particular the interval valued q fuzzy hyperideals in a hyperring will be investigated moreover we also consider the concept of implication based interval valued fuzzy hyperideals in a hyperring some recent results obtained by b davvaz and j m zhan on hyperstructures are extended and consolidated

on the definition of a fuzzy subgroup abstract using the idea of quasi coincidence of a fuzzy point with a fuzzy set some new concepts of a fuzzy subgroup are introduced and their acceptibility is investigated some fundamental properties of one such viable fuzzy subgroup are obtained

a mimetic discretization of the reissner mindlin plate bending problem we present a mimetic approximation of the reissner mindlin plate bending problem which uses deflections and rotations as discrete variables the method applies to very general polygonal meshes even with non matching or non convex elements we prove linear convergence for the method uniformly in the plate thickness

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

optimal control of quasilinear parabolic equations this paper deals with optimal control problems governed by quasilinear parabolic equations in divergence form whose cost functional is of lagrangian type our aim is to prove the existence of solutions and derive some optimality conditions to attain this second objective we accomplish the sensitivity analysis of the state equation with respect to the control proving that under some assumptions this relation is g teaux differentiable finally a regularising procedure along with ekeland s variational principle allow us to treat some other problems for which this differentiability property cannot be stated

generalized fuzzy groups and many valued implications in this paper we give the definition of a fuzzy subgroup with thresholds which is a generalization of rosenfeld s fuzzy subgroup and bhakat and das s fuzzy subgroup we also give the definition of an implication based fuzzy subgroup and discuss relations between two fuzzy subgroups

level subgroups and union of fuzzy subgroups abstract in this paper we investigate the conditions under which a given fuzzy subgroup of a given group can or can not be realized as a union of two proper fuzzy subgroups moreover we formulate the notion of fuzzy subgroup generated by a given fuzzy subset by level subgroups we also give characterizations of fuzzy conjugate subgroups and fuzzy characteristic subgroups by their level subgroups also we discuss the relationship between level subgroups of a given fuzzy subgroup and the level subgroups of its homomorphic image

some kinds of c ccq interval valued fuzzy ideals of bci algebras in this paper we first introduce the notions of positive implicative implicative and commutative interval valued fuzzy ideals of bci algebras which are generalizations of positive implicative implicative and commutative fuzzy ideals respectively and investigate some of their related properties the concept of quasi coincidence of an interval valued fuzzy point within an interval valued fuzzy set is introduced in fact the concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we further introduce the notions of positive implicative implicative and commutative q interval valued fuzzy ideals of bci algebras and investigate some of their related properties some characterization theorems of these generalized interval valued fuzzy ideals are derived the relationship among these generalized interval valued fuzzy ideals of bci algebras is also considered

higher order mimetic methods for unstructured meshes a higher order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer mimetic discretization methods create discrete versions of the partial differential operators such and the gradient and divergence that are exact in some sense and therefore mimic the important mathematical properties of their continuous counterparts the proposed numerical method is an interesting mixture of both finite volume and finite element ideas while the ideas presented can be applied to arbitrarily high order accuracy we focus in this work on the details of creating a third order accurate method the proposed method is shown to be exact for piecewise quadratic solutions and shows third order convergence on arbitrary triangular tetrahedral meshes the numerical accuracy of the method is confirmed on both two dimensional and three dimensional unstructured meshes the computational cost required for a desired accuracy is analyzed against lower order mimetic methods

mimetic finite difference method for the stokes problem on polygonal meshes various approaches to extend finite element methods to non traditional elements general polygons pyramids polyhedra etc have been developed over the last decade the construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis the mimetic finite difference mfd method works on general polygonal meshes and has many similarities with low order finite element methods both schemes try to preserve the fundamental properties of the underlying physical and mathematical models the essential difference between the two schemes is that the mfd method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices since no extension of basis functions inside the mesh elements is required practical implementation of the mfd method is simple for polygonal meshes that may include degenerate and non convex elements in this article we present a new mfd method for the stokes problem on arbitrary polygonal meshes and analyze its stability the method is developed for the general case of tensor coefficients which allows us to apply it to a linear elasticity problem as well numerical experiments show for the velocity variable second order convergence in a discrete l 2 norm and first order convergence in a discrete h 1 norm for the pressure variable first order convergence is shown in the l 2 norm

soft bl algebras based on fuzzy sets by means of soft sets and q soft sets some characterizations of implicative positive implicative and fantastic filteristic soft bl algebras are investigated finally we prove that a soft set is an implicative filteristic soft bl algebra if and only if it is both a positive implicative filteristic soft bl algebra and a fantastic filteristic soft bl algebra

optimal control problems governed by some semilinear parabolic equations abstract this paper is concerned with the optimal control problem for the keller segel equations that is as a generalization of ryu and yagi j math anal appl 256 2001 45 66 we derive the optimality conditions for the optimal control problem governed by a semilinear abstract equation of nonmonotone type moreover we prove the uniqueness of the optimal control under some conditions

some kinds of fuzzy ideals of bci algebras the concepts of c c q d fuzzy positive implicative implicative and commutative ideals and c c q d fuzzy positive implicative implicative and commutative ideals in bci algebras are introduced some new characterizations are investigated in particular we prove that a fuzzy set m of a bci algebra x is an c c q d fuzzy implicative ideal of x if and only if it is both an c c q d fuzzy positive implicative ideal and an c c q d fuzzy commutative ideal finally we give some characterizations of three particular classes of bci algebras by these generalized fuzzy ideals

redefined fuzzy implicative filters using the belongs to relation and quasi coincidence with relation q between fuzzy points and fuzzy sets the concept of q j fuzzy implicative filters where q j are any two of q email protected q email protected q with q email protected q is introduced and related properties are discussed relations between email protected q email protected q fuzzy implicative filters and email protected q fuzzy implicative filters are investigated and conditions for an email protected q fuzzy implicative filter to be an fuzzy implicative filter are provided characterizations of email protected q fuzzy implicative filters are given and conditions for a fuzzy set to be a q email protected q fuzzy implicative filter are provided

a preconditioned multilevel mimetic finite difference method for solving the pressure velocity system abstract a mimetic finite difference mfd implementation is proposed to solve the pressure velocity system iteratively the recursive procedure only solves for the velocity variable while the pressure is calculated by direct substitution simplifying the problem the symmetric positive definite system obtained is solved with an innovative implementation of a pre conditioned multilevel conjugate gradient algorithm where coarse algebraic objects are easily computed from the corresponding fine level ones based on fundamental geometric properties of the mfd technology a succinct eigen analysis shows second order convergence on the velocity variable for cartesian grids which is corroborated numerically also results consider different topologies and different medium properties showing the applicability of the method and optimal convergence rates for the velocity on cartesian and h 2 uniform curved grids

fuzzy n ary polygroups related to fuzzy points recently fuzzy n ary sub polygroups were introduced and studied by davvaz corsini and leoreanu fotea b davvaz p corsini v leoreanu fotea fuzzy n ary sub polygroups comput math appl 57 2008 141 152 now in this paper the concept of email protected q fuzzy n ary sub polygroups email protected email protected email protected email protected fuzzy n ary sub polygroups and fuzzy n ary sub polygroup with thresholds of an n ary polygroup are introduced and some characterizations are described also we give the definition of implication based fuzzy n ary sub polygroups in an n ary polygroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

nonconvex optimal control of nonlinear monotone parabolic systems abstract an optimal control problem is studied for distributed systems governed by nonlinear parabolic pde s with state constraints the state equation is monotone in the state variable and nonlinear in the control variable the constraints and the cost functional are not necessarily convex relaxed controls are used to prove the existence of an optimal control moreover a minimum principle of relaxed optimality is established

analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems the maximum principle is one of the most important properties of solutions of partial differential equations its numerical analog the discrete maximum principle dmp is one of the most difficult properties to achieve in numerical methods especially when the computational mesh is distorted to adapt and conform to the physical domain or the problem coefficients are highly heterogeneous and anisotropic violation of the dmp may lead to numerical instabilities such as oscillations and to unphysical solutions such as heat flow from a cold material to a hot one in this work we investigate sufficient conditions to ensure the monotonicity of the mimetic finite difference mfd method on two and three dimensional meshes these conditions result in a set of general inequalities for the elements of the mass matrix of every mesh element efficient solutions are devised for meshes consisting of simplexes parallelograms and parallelepipeds and orthogonal locally refined elements as those used in the amr methodology on simplicial meshes it turns out that the mfd method coincides with the mixed hybrid finite element methods based on the low order raviart thomas vector space thus in this case we recover the well established conventional angle conditions of such approximations instead in the other cases a suitable design of the mfd method allows us to formulate a monotone discretization for which the existence of a dmp can be theoretically proved moreover on meshes of parallelograms we establish a connection with a similar monotonicity condition proposed for the multi point flux approximation mpfa methods numerical experiments confirm the effectiveness of the considered monotonicity conditions

ϵ q level subset abstract the notion of q level subset is introduced the study of q level subset of an q fuzzy subgroup subring or ideal are dealt with

equivalent projectors for virtual element methods in the original virtual element space with degree of accuracy k projector operators in the h 1 seminorm onto polynomials of degree k can be easily computed on the other hand projections in the l 2 norm are available only on polynomials of degree k 2 directly from the degrees of freedom here we present a variant of the virtual element method that allows the exact computations of the l 2 projections on all polynomials of degree k the interest of this construction is illustrated with some simple examples including the construction of three dimensional virtual elements the treatment of lower order terms the treatment of the right hand side and the l 2 error estimates

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

more on fuzzy lattices in this paper the concept of an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter in a lattice is introduced which is a generalization of the concept as given by davvaz and kazanci 2011 18 characterizations for an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are provided different classes of lattices are characterized by the properties of these fuzzy sublattices ideals filters using the notions of a fuzzy sublattice ideal filter with thresholds characterization of a fuzzy sublattice ideal filter an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are discussed

on the optimal control of strongly nonlinear evolution equations abstract in this paper we study optimal control problems governed by nonlinear evolution equations with nonmonotone nonlinearities in the state first we prove an existence theorem then using the penalty method we obtain necessary conditions for optimality from them we derive a bang bang characterization of optimal controls finally an example of a nonlinear parabolic optimal control system is worked out in detail

fuzzy filters and fuzzy prime filters of bounded r l monoids and pseudo bl algebras the logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics the sets of provable formulas in corresponding inference systems from the point of view of uncertain information can be described by fuzzy filters of those algebraic semantics bounded residuated lattice ordered monoids email protected monoids are a common generalization of pseudo bl algebras and consequently of pseudo mv algebras and heyting algebras i e algebras behind fuzzy and intuitionistic reasoning in the paper we introduce and investigate fuzzy filters of bounded email protected monoids and fuzzy prime filters of pseudo bl algebras

characterizations of regular ordered semigroups in terms of α β fuzzy generalized bi ideals in this paper the concept of an a b fuzzy generalized bi ideal in an ordered semigroup is introduced which is a generalization of the concept of a fuzzy generalized bi ideal in an ordered semigroup using this concept some characterization theorems are provided the upper lower parts of an q fuzzy generalized bi ideal are introduced and some characterizations of regular ordered semigroups are given also we consider the concept of implication based fuzzy generalized bi ideals in an ordered semigroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

generalized fuzzy interior ideals in semigroups using the idea of quasi coincidence of a fuzzy point with a fuzzy set the concept of an a b fuzzy interior ideal which is a generalization of a fuzzy interior ideal in a semigroup is introduced and related properties are investigated

distributed control of systems governed by a general class of quasilinear elliptic equations abstract in this paper we are concerned with optimal control problems governed by a general class of quasilinear elliptic equations our aim is to prove existence of solution and derive optimality conditions in order to deal with this last question we begin investigating differentiability of state solution of equation with respect to the control second term of equation obtaining it only in certain cases a perturbation method is used to treat other cases as a consequence of the optimality system regularity of optimal control and state is establised

algebraic multigrid preconditioning of high order spectral elements for elliptic problems on a simplicial mesh algebraic multigrid is investigated as a solver for linear systems that arise from high order spectral element discretizations an algorithm is introduced that utilizes the efficiency of low order finite elements to precondition the high order method in a multilevel setting in particular the efficacy of this approach is highlighted on simplexes in two and three dimensions with nodal spectral elements up to order n 11 additionally a hybrid preconditioner is also developed for use with discontinuous spectral element methods the latter approach is verified for the discontinuous galerkin method on elliptic problems

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity

fuzzy subgroup some characterizations ii abstract we consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups given a finite chain of subgroups of a group g we prove that there exists a fuzzy subgroup of g whose level subgroups are exactly the subgroups of this chain as a corollary we obtain an interpretation of the number of chains of subgroups of a group g in which a subgroup h is a member when the group g is a supersolvable group some further interpretation of this number is obtained