critical exponents of self avoiding walks on a family of truncated n simplex lattices the authors have studied self avoiding walks saws on a family of truncated n simplex lattices which provide a family of fractals in which the fractal dimension d can be varied to a wide range while the spectral dimension d is held almost fixed by means of exact renormalisation group transformations they have calculated the critical exponents nu alpha and gamma and the connectivity constant mu of the saws for n 5 and 6 they propose an approximate theory for calculating the critical exponents of the saws on fractals which is expected to be accurate at large values of n they show that the theory gives results which are in good agreement with exact values even for small values of n and leads to simple closed relations for the exponents

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

speculations on self avoiding surfaces in fractals a mean field treatment the authors estimate the exponents characterising the self avoiding surfaces using an approximation in the framework of a flory type theory they find for planar self avoiding surfaces embedded randomly in a fractal of dimensionality d nu 3 4 d for random surfaces of fractal dimension d embedded in a euclidean space of dimensionality d nu 3 2d d 2 and for fractal surfaces embedded in a structure of fractal dimensionality d nu 3 2d d 2

correction to scaling exponents and amplitudes for the correlation length of linear polymers in two dimensions we consider the scaling behaviour of the radius of gyration for a system of dilute linear polymers we focus on pn the mean square end to end distance of an n step self avoiding walk for which an additional two terms were recently calculated for the close packed triangular lattice combining several extrapolation methods we find that a consistent description of the scaling behaviour exists if and only if the correction to scaling exponent a is roughly half as large as commonly believed we conclude that all data ale consistent with the equation pn an2 1 b na c n where y a a 1 j2 abso 21 and c lo

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

approximations in hypergroups and fuzzy hypergroups the first part of this paper represents a continuation of the study of approximations in a hypergroup we analyse the lower and upper approximations of a subset in a hypergroup with respect to some operators particularly the completeness operator in the last part we introduce and analyse the lower and upper approximation of a subset in a fuzzy hypergroup

self avoiding walks on random networks of resistors and diodes abstract we study the self avoiding walks saw on a square lattice whose various degrees of randomness encompasses many different random networks including the incipient clusters of the directed mixed and isotropic bond percolation we apply the position space renormalization group psrg method and demonstrate that within the framework of this method one is bound to find that the critical exponent v of the mean end to end distance of saw on various two dimensional random networks should be equal to the critical exponent of saw on the ordinary square lattice a detailed analysis of this finding and similar findings of other authors lead us to conclude that a debatable opposite finding which has been predicted on the basis of different approaches could be attained after a substantial refinement of the method applied

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

on fuzzy congruence of a near ring module the aim of this paper is to introduce fuzzy submodule and fuzzy congruence of an r module near ring module to obtain the correspondence between fuzzy congruences and fuzzy submodules of an r module to define quotient r module of an r module over a fuzzy submodule and to obtain correspondence between fuzzy congruences of an r module and fuzzy congruences of quotient r module over a fuzzy submodule of an r module

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

position space renormalisation group for isolated polymer chains we develop a cell position space renormalisation group psrg with which we study the scaling properties of isolated polymer chains we model a chain by a self avoiding walk constrained to a lattice for rescaling factors b s 6 we calculate recursion relations analytically on the square lattice with several different choices for the psrg weight function we also calculate implicit cell to cell transformations in which a cell of size b is rescaled to a cell of size b the results of these psrgs improve both as b increases and as b b 1 in addition we construct a true infinitesimal psrg transformation which appears to become exact as the dimensionality d approaches 1 we obtain the closed form expression for the correlation length exponent u d l d in d the flory formula deviates from this already at first order in d 1 we also develop a constant fugacity monte carlo method which enables us to simu late in an unbiased way within the grand canonical ensemble chains of up to lo3 bonds with this method we extend the psrg to larger cells b s 150 on the square lattice our numerical method provides high statistical accuracy for all cell sizes however in the range of b we study the asymptotic behaviour of our results appears to depend on the choice of weight function one weight function provides smooth behaviour as a function of b and with it we extrapolate to find u 0 756 0 004 further work is required to resolve the apparent anomalies in the results based on the other weight functions

fuzzy h v groups in this paper we introduce the concept of fuzzy subhypergroup of a hypergroup as well as the fuzzy hv group we prove some results in this respect we also consider the fundamental relation defined on an hv group h and for a fuzzy subset of h we define the fuzzy subset of h and prove a fundamental theorem concerning the group h

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

rosenfeld s fuzzy subgroups with interval valued membership functions abstract in this paper we define interval valued fuzzy subgroups i e i v fuzzy subgroups of rosenfeld s nature a necessary and sufficient condition for an i v fuzzy subset to be an i v fuzzy subgroup is stated intersection of two i v fuzzy subgroups is also an i v fuzzy subgroup the images and inverse images of i v fuzzy subgroups are defined and how the images or inverse images of i v fuzzy subgroups become i v fuzzy subgroups is studied

orthogonal spline collocation methods for partial differential equations abstract this paper provides an overview of the formulation analysis and implementation of orthogonal spline collocation osc also known as spline collocation at gauss points for the numerical solution of partial differential equations in two space variables advances in the osc theory for elliptic boundary value problems are discussed and direct and iterative methods for the solution of the osc equations examined the use of osc methods in the solution of initial boundary value problems for parabolic hyperbolic and schrodinger type systems is described with emphasis on alternating direction implicit methods the osc solution of parabolic and hyperbolic partial integro differential equations is also mentioned finally recent applications of a second spline collocation method modified spline collocation are outlined

self avoiding walks on fractals studied by the monte carlo renormalization group the authors have applied the monte carlo renormalization group mcrg method to study the problem of self avoiding walks on the sierpinski gasket family of fractals each member of the family is labelled by an integer b 2 or b or infinity and when b to infinity both the fractal df and spectral ds dimension approach their euclidean value 2 they have calculated the critical exponent nu associated with the mean square end to end distance up to b 80 their mcrg results deviate at most 0 03 from the available exact results for 2 or b or 9 the obtained data show clearly that nu monotonically decreases with b and crosses the euclidean value nu 3 4 at b approximately 27 that is before entering the fractal to euclidean crossover region that occurs in the limit b to infinity

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

a new type of fuzzy n ary hyperstructures the aim of this paper is to consider and study a new kind of fuzzy n ary hyperstructures such as fuzzy n ary hypergroups and fuzzy m n ary hyperrings

superuniversal spectral dimension for dilute branched polymers the authors introduce the problem of random walks on lattice animals dilute branched polymers and calculate the spectral dimension ds of animals in two and three dimensions by using a two parameter position space renormalisation group method this problem which is a generalisation of the problem of the ant in the labyrinth has been independently proposed and investigated by wilke et al 1984 the spectral dimension is given by ds 2da dw where da is the fractal dimension of the lattice animal and dw the fractal dimension of the random walk on the lattice animal the results indicate that ds may be a superuniversal quantity i e its value is independent of dimension moreover the authors find ds to be close to 4 3 which is the spectral dimension of the largest percolation cluster at the percolation threshold pc as conjectured by alexander and orbach 1982 since both lattice animals and the largest percolation cluster at pc have a homogeneous interior structure the results suggest that the spectral dimension of all such fractals may equal 4 3

critical exponents of the self avoiding walks on a family of finitely ramified fractals the authors have studied the self avoiding walks saw on a family of finitely ramified fractals the first member b 2 of the family is the two dimensional sierpinski gasket while the last member b infinity appears to be a wedge of the homogeneous triangular lattice by means of the exact renormalisation group transformations they have calculated the critical exponents alpha nu and gamma and the connectivity constant mu of saw on each member of a sequence 2 or b or 8 of the studied fractal family the obtained exact results are compared with the recent phenomenological proposals and with the results believed to be exact in the case of a homogeneous two dimensional lattice

fuzzy γ hypernear rings the concept of c hypernear rings which is a generalization of c near rings and hypernear rings is introduced some related properties of c hypernear rings are described in particular three isomorphism theorems of c hypernear rings are established by using this new idea we consider the fuzzy hyperideals of c hypernear rings finally the fundamental relations between c hypernear rings and c near rings are discussed

fuzzy subrings and ideals redefined abstract v q fuzzy subrings and ideals of a ring are defined the concepts of v q fuzzy semiprime prime semi primary primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained v q fuzzy cosets determined by v q fuzzy ideals and v q fuzzy radicals of v q fuzzy ideals are discussed

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

on probabilistic n ary hypergroups abstract the t fuzzy n ary subhypergroups of an n ary hypergroup are defined by using triangular norms and some related properties are hence obtained in particular we consider the probabilistic version of n ary hypergroups by using random sets and show that the fuzzy n ary hypergroups defined by triangular norms are consequences of some probabilistic n ary hypergroups under certain conditions some results on n ary hypergroups recently given by davvaz and corsini are extended

characterizations of ordered semigroups by the properties of their fuzzy ideals in this paper we characterize different classes of ordered semigroups by the properties of their ideals quasi ideals and bi ideals we also characterize these classes by the properties of their fuzzy ideals fuzzy quasi ideals and fuzzy bi ideals

roughness in modules the theory of rough sets was proposed by pawlak in 1982 the relations between rough sets and algebraic systems have been already considered by many mathematicians important algebraic structures are groups rings and modules rough groups and rough rings have been investigated by biswas and nanda kuroki and wang and davvaz in this paper we consider an r module as a universal set and we introduce the notion of rough submodule with respect to a submodule of an r module which is an extended notion of a submodule in an r module we also give some properties of the lower and the upper approximations in an r module

a point to segment contact formulation for isogeometric nurbs based finite elements formulation of isogeometric finite elements has received a great deal of attention in the recent past the present study deals with the treatment of problems in structural mechanics including large elastic deformations and contact one decisive difference between isogeometric finite elements based on nurbs functions and standard finite elements fe based on lagrange polynomials is higher inter element continuity this is a promising characteristics to model contact problems as all issues associated with kinks between elements are naturally avoided particularly in cases with large sliding this has the potential to be an attractive feature we present a bilateral isogeometric collocation contact formulation for geometrically non linear two dimensional problems using greville and botella points to collocate the contact integrals different methods to obtain accurate and physically meaningful stress distributions are investigated and compared the results show that the higher inter element continuity in context of non smooth problems may imply undesired effects in the numerical solution such as unphysical stress oscillations similar effects have been observed in standard p fem numerical experiments indicate that these oscillations may be avoided if the basis functions of contact and non contact zones are separated by knot relocation and knot repetition

parisi s mean field solution for spin glasses as an analytic continuation in the replica number parisi s replica symmetry breaking solution for spin glasses is extended to finite replica number n the free energy fp n obtained this way as well as its first two derivatives with respect to n are shown to join the corresponding values in the sherrington kirkpatrick sk solution at a characteristic value ns t where stability breaks down in the latter the continuation composed of the sk branch fsk n for n or ns t and the parisi branch fp n for 0 or n or ns t fulfils the requirements of convexity monotonicity and stability for all n

integration free coons macroelements for the solution of 2d poisson problems large isoparametric macroelements with closed form cardinal global shape functions under the label coons patch macroelements cpm have been previously proposed and used in conjunction with the finite element method and the boundary element method this paper continues the research on the performance of cpm in conjunction with the collocation method in contrast to the previous cpm that was based on a galerkin ritz formulation no domain integration is now required a fact that justifies the name integration free coons macroelements therefore in addition to avoiding mesh generation and saving human effort the proposed technique has the additional advantage of further reducing the computer effort the theory is supported by five test cases concerning poisson and laplace problems within 2d smooth quadrilateral domains copyright 2008 john wiley sons ltd

exact series studies of self avoiding walks on two dimensional critical percolation clusters the author presents results of exact series studies of self avoiding walks on percolation clusters on the square lattice performed very close to the percolation threshold and estimates the critical exponents nu and gamma defined by the disorder averages of the mean square radius of gyration or the end to end distance and the number of self avoiding walks respectively the self avoiding walk configurations are enumerated exactly up to 35 steps the result for nu indicates a large increase compared with the self avoiding walks on fully occupied lattice the result for gamma however indicates a behaviour similar to that on a fully occupied lattice the result for nu is completely different from that of lee nakanishi and kim 1989

on fuzzy subnear rings and ideals abstract the aim of this paper is to introduce the notion of a fuzzy subnear ring to study fuzzy ideals of a near ring and to give some properties of fuzzy prime ideals of a near ring

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

on fuzzy isomorphism theorems of γ hyperrings in this paper we first derive three isomorphism theorems and a jordan holder theorem of c hyperrings by fuzzy c hyperideals we establish three fuzzy isomorphism theorems of c hyperrings

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

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

diffusion on percolation clusters at criticality the concept of fractal dimensionality is used to study the problem of diffusion on percolation clusters the authors find from monte carlo simulations that the fractal dimensionality of a random walk on a critical percolation cluster in three dimensional space is d 3 3 or 0 1 where the size of the cluster is restricted to be larger than the span of the walk and is d 3 9 or 0 1 for a walk on clusters not subject to this restriction for two dimensional space they find d approximately d approximately 2 7 or p0 1 the exponent d and d is related to the scaling of the average length r of n steps via rd varies as n the fracton dimensionality which is related to the density of states was found to be 1 26 or 0 1 these results are in good agreement with the predictions of alexander and orbach 1982

a high order b spline collocation method for linear boundary value problems abstract collocation methods are investigated because of their simplicity and inherent efficiency for applications to linear boundary value problems on a b the objective of the present research is obtaining numerical solution of the boundary value problems for d th order linear boundary value problem by a b spline collocation method using b splines of order k and their index of regularity is m d 1 m k 2 the collocation points in our method form a strictly increasing sequence of points in a b each interior j th collocation point belongs to the interior of the compact support of corresponding j th b spline basis element and the number of b spline basis elements equals the number of collocation points the order of accuracy of the proposed method is shown to be optimal the mathematical properties of this collocation method are less well established primarily because the order of accuracy depends on the regularity and order of b spline basis and location of the collocation points the error analysis is through the green s function approach than the matrix approach we compare the efficiency and accuracy of our method to nodal and orthogonal collocation methods as applied to linear ordinary differential equations with boundary conditions our collocation method like greville collocation method is more convenient than nodal or orthogonal collocation because exactly the correct number of collocation points is available the greville and botella collocation methods are special cases of our collocation method

numerical method using cubic b spline for the heat and wave equation in the present paper the cubic b splines method is considered for solving one dimensional heat and wave equations a typical finite difference approach had been used to discretize the time derivative while the cubic b spline is applied as an interpolation function in the space dimension the accuracy of the method for both equations is discussed the efficiency of the method is illustrated by some test problems the numerical results are found to be in good agreement with the exact solution

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

where two fractals meet the scaling of a self avoiding walk on a percolation cluster the scaling properties of self avoiding walks on a d dimensional diluted lattice at the percolation threshold are analyzed by a field theoretical renormalization group approach to this end we reconsider the model of y meir and a b harris phys rev lett 63 2819 1989 and argue that via renormalization its multifractal properties are directly accessible while the former first order perturbation did not agree with the results of other methods our analytic result gives an accurate description of the available mc and exact enumeration data in a wide range of dimensions 2 ensuremath leqslant d ensuremath leqslant 6

lattice structure on fuzzy congruence relations of a hypergroupoid in this manuscript we first define the notion of fuzzy left right congruence relation on a hypergroupoid and then we investigate the lattice structure of the set of these fuzzy relations finally we show that a special class of fuzzy equivalence relations on the hypergroupoid forms a distributive lattice

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

exact fractals with adjustable fractal and fracton dimensionalities a family of exact fractals is presented by adjusting two external parameters a wide range of fractal and fracton dimensionalities can be achieved this includes the case of fracton dimensionality of 2 which is critical for diffusion

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

diffusion on random systems above below and at their percolation threshold in two and three dimensions a detailed monte carlo study is presented for classical diffusion random walks on random l l triangular and l l l simple cubic lattices with l up to 4096 and 256 respectively the speed of a cyber 205 vector computer is found to be about one order of magnitude larger than that of a usual cdc cyber 76 computer to reach the asymptotic scaling regime walks with up to 10 million steps were simulated with about 10 jl steps in total for l 256 at the percolation threshold we review and extend the dynamical scaling description for the distance traveled as function of time the diffusivity above the threshold and the cluster radius below earlier discrepancies between scaling theory and computer experiment are shown to be due to insufficient monte carlo data the conductivity exponent is found to be 2 0 0 2 in three and 1 28 0 02 in two dimensions our data in three dimensions follow well the finite size scaling theory below the threshold the approach of the distance traveled to its asymptotic value is consistent with theoretical speculations and an exponent 2 5 independent of dimensionality the correction to scaling exponent at pc seems to be larger in two than in three dimensions

isogeometric collocation cost comparison with galerkin methods and extension to adaptive hierarchical nurbs discretizations abstract we compare isogeometric collocation with isogeometric galerkin and standard c 0 finite element methods with respect to the cost of forming the matrix and residual vector the cost of direct and iterative solvers the accuracy versus degrees of freedom and the accuracy versus computing time on this basis we show that isogeometric collocation has the potential to increase the computational efficiency of isogeometric analysis and to outperform both isogeometric galerkin and standard c 0 finite element methods when a specified level of accuracy is to be achieved with minimum computational cost we then explore an adaptive isogeometric collocation method that is based on local hierarchical refinement of nurbs basis functions and collocation points derived from the corresponding multi level greville abscissae we introduce the concept of weighted collocation that can be consistently developed from the weighted residual form and the two scale relation of b splines using weighted collocation in the transition regions between hierarchical levels we are able to reliably handle coincident collocation points that naturally occur for multi level greville abscissae the resulting method combines the favorable properties of isogeometric collocation and hierarchical refinement in terms of computational efficiency local adaptivity robustness and straightforward implementation which we illustrate by numerical examples in one two and three dimensions

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

fuzzy hv submodules abstract in this paper we define the concept of fuzzy h v submodule of an h v module and study a few results in this respect we also consider the fundamental relation e defined on an h v module m and prove a fundamental theorem concerning the module m e

self avoiding walks on percolation clusters the author studies self avoiding walks saws on percolation clusters a scaling function representation for r the mean end to end distance is proposed which describes a crossover from ordinary saws to saws on fractals he distinguishes between saws on a single cluster for which r approximately nx where x nu 1 and saws on all clusters for which r approximately nz where z nu 2 and n is the number of monomers in the walk he estimates nu 1 d 2 approximately 1 285 and the correction to scaling exponent omega d 2 approximately 1 3 and nu 1 d 3 approximately 1 38 two plausible generalisations of the flory 1953 approximation for nu 1 are investigated and it is argued that none of them provides a satisfactory approximation for nu 1 at all dimensions

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

the backbone and conductivity of random clusters the author studies the properties of the backbone of and conduction in random clusters which have homogeneous interior structure these include the largest percolation cluster at pc lattice animals and the witten sander ws aggregates for lattice animals the fractal dimension da of the backbone is estimated the for first time and is found to be about 1 14 at d 2 and about 1 39 at d 3 these values are much lower than the corresponding values for the animals themselves the fractal and spectral dimensions of the backbone of the ws aggregates are estimated to be about 1 25 and 1 06 at d 2 respectively a recent hypothesis which relates the fractal dimension of random walks on these clusters to those of the clusters and their backbones is also discussed it is shown that for the ws aggregates ds ds 2 on a bethe lattice i e at d infinity in contrast with ds 4 3 and ds 1 for percolation clusters and lattice animals the conductivity exponent ta of lattice animals is found to be ta d 2 approximately 0 73 and ta d 3 approximately 1 19 and ta d or 8 2 whereas for the ws aggregates the author finds tws d 2 approximately 0 67 and tws d 3 approximately 0 94 and tws d to infinity 1

fuzzy h ideals of hemirings a characterization of an h hemiregular hemiring in terms of a fuzzy h ideal is provided some properties of prime fuzzy h ideals of h hemiregular hemirings are investigated it is proved that a fuzzy subset z of a hemiring s is a prime fuzzy left right h ideal of s if and only if z is two valued z 0 1 and the set of all x in s such that z x 1 is a prime left right h ideal of s finally the similar properties for maximal fuzzy left right h ideals of hemirings are considered

scaling theory for the statistics of self avoiding walks on random lattices the authors study self avoiding walks saw on randomly diluted quenched lattices with direct configurational averaging over the moments of the saw distribution function a scaling function representation of rn the average end to end distance of n step walks is studied here both for saw on a the infinite percolation cluster and b any cluster they have shown that at the percolation threshold nu p nu p 1 beta p 2 nu p where beta p and nu p are the percolation order parameter and correlation length exponents respectively the authors also propose a scaling function representation for the total number of n step saw configuration gn approximately mu nngamma 1 for infinite cluster averaging which gives gamma p gamma d nu p nu for all cluster averaging gamma will remain unchanged

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained