long route to consensus two stage coarsening in a binary choice voting model formation of consensus in binary yes no type of voting is a well defined process however even in presence of clear incentives the dynamics involved can be incredibly complex specifically formations of large groups of similarly opinionated individuals could create a condition of support bubbles or spontaneous polarization that renders consensus virtually unattainable e g the question of the uk exiting the eu there have been earlier attempts in capturing the dynamics of consensus formation in societies through simple z 2 symmetric models hoping to capture the essential dynamics of average behavior of a large number of individuals in a statistical sense however in absence of external noise they tend to reach a frozen state with fragmented and polarized states i e two or more groups of similarly opinionated groups with frozen dynamics here we show in a kinetic exchange opinion model considered on l l square lattices that while such frozen states could be avoided an exponentially slow approach to consensus is manifested specifically the system could either reach consensus in a time that scales as l 2 or a long lived metastable state termed a domain wall state for which formation of consensus takes a time scaling as l 3 6 the latter behavior is comparable to some voterlike models with intermediate states studied previously the late time anomaly in the timescale is reflected in the persistence probability of the model finally the interval of zero crossing of the average opinion i e the time interval over which the average opinion does not change sign is shown to follow a scale free distribution which is compared with that seen in the opinion surveys regarding brexit and associated issues since the late 1970s the issue of minority spreading is also addressed by calculating the exit probability

on fuzzy spaces and fuzzy group theory abstract the concept of fuzzy space is introduced this concept corresponds to the concept of the universal set in the ordinary case the algebra of fuzzy spaces and fuzzy subspaces is studied using the concept of fuzzy space and fuzzy binary operation a new approach to study fuzzy group theory is given this approach can be considered as a generalization and reformulation of the rosenfeld theory of fuzzy subgroups therefore it is an active tool to develop the theory of fuzzy groups

zero temperature glauber dynamics on small world networks the zero temperature glauber dynamics of the ferromagnetic ising model on small world networks rewired from a two dimensional square lattice has been studied by numerical simulations for increasing disorder in finite networks the nonequilibrium dynamics becomes faster so that the ground state is found more likely for any finite value of the rewiring probability p the likelihood of reaching the ground state goes to zero in the thermodynamic limit similarly to random networks the spin correlation r is found to decrease with distance as r exp r being a correlation length scaling with p as p 0 73 these results are compared with those obtained earlier for addition type small world networks

inference of fuzzy relational tableaux from fuzzy exemplifications the paper describes a method for deriving fuzzy relational tableaux from fuzzy exemplifications in particular the work by thole zimmerman and zysno 4 is cited as they derive an operator for and using data derived from human subjects the method results in an operator or operators which is a maximal restriction of the operators implied by the data results showing the process are described and a value of and is derived using data presented in 4

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

a solution to an open problem on the t product of tl fuzzy subgroups many studies have investigated necessary and sufficient conditions whereby fuzzy subgroups of a cartesian product of groups are a cartesian product of fuzzy subgroups chon fuzzy subgroups as products fuzzy sets and systems 141 2004 505 508 found such conditions under minimum operation he pointed out that the problem of finding necessary and sufficient conditions for t fuzzy subgroups under a t norm operation is still open in this study we solve the problem and identify necessary and sufficient conditions under t norm operation

a class of stochastic games with infinitely many interacting agents related to glauber dynamics on random graphs we introduce and study a class of infinite horizon non zero sum non cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics first we show in the general case of asymmetric interactions the existence of a strategy that allows any player to eliminate losses after a finite random time in the special case of symmetric interactions we also prove that as time goes to infinity the game converges to a nash equilibrium moreover assuming that all agents adopt the same strategy using arguments related to those leading to perfect simulation algorithms spatial mixing and ergodicity are proved in turn ergodicity allows us to prove fixation i e players will adopt a constant strategy after a finite time the resulting dynamics is related to zero temperature glauber dynamics on random graphs of possibly infinite volume

fuzzy sylow subgroups abstract an attempt is made to define a fuzzy sylow p subgroup of a finite group some basic results regarding sylow p subgroups are extended to the fuzzy setting in particular fuzzy versions of sylow s theorems are obtained

abelian fuzzy group and its properties abstract the concepts of abelian fuzzy group torsion fuzzy group torsion free fuzzy group and mixed fuzzy group are introduced the properties of these fuzzy groups and their relations are discussed

on t fuzzy subfield and t fuzzy vector subspaces abstract in this paper we improve the definition of t fuzzy subfield and observe some of its properties the concept of t fuzzy vector subspaces of a t fuzzy subfield of a field will also be investigated and we further introduce the concept of t fuzzy subalgebra

field theory of bicritical and tetracritical points iv critical dynamics including reversible terms this article concludes a series of papers folk holovatch and moser phys rev e 78 041124 2008 78 041125 2008 79 031109 2009 where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points here we give the complete two loop calculation and analysis of the dynamic renormalization group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field we find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way this holds independent whether the heisenberg fixed point or the biconical fixed point in statics is the stable one the nonasymptotic analysis of the dynamic flow equations shows that due to cancellation effects the critical behavior is described in distances from the critical point accessible to experiments by the critical behavior qualitatively found in one loop order although one may conclude from the effective dynamic exponents taking almost their one loop values that weak scaling for the order parameter components is valid the flow of the time scale ratios is quite different and they do not reach their asymptotic values

nonequilibrium critical relaxation with coupling to a conserved density the authors study nonequilibrium critical relaxation properties of model c purely dissipative relaxation of an order parameter coupled to a conserved density starting from a macroscopically prepared initial state with short range correlations using a field theoretic renormalization group approach they show that all the stages of growth of the correlation length display universal behaviour governed by a new critical exponent theta this exponent is calculated to second order in in 4 d where d is the spatial dimension of the system

zero temperature dynamics for the ferromagnetic ising model on random graphs abstract we consider glauber dynamics at zero temperature for the ferromagnetic ising model on the usual random graph model on n vertices with on average edges incident to each vertex in the limit as n based on numerical simulations svenson phys rev e 64 2001 036122 reported that the dynamics fails to reach a global energy minimum for a range of values of the present paper provides a mathematically rigorous proof that this failure to find the global minimum in fact happens for all 0 a lower bound on the residual energy is also given

fuzzy subgroups as union of two fuzzy subgroups abstract the problem of writing a fuzzy subgroup of a group g as a union of two fuzzy subgroups has been discussed by dixit et al in this paper an attempt has been made to study this problem further in a broader framework of nontrivial decomposition of a fuzzy subgroup thus something more than the settlement of the question of the possibility of having nonequivalent fuzzy subgroups in this union raised by the author at the end of the section 3 of their paper has been proved

the properties of fuzzy divisible groups abstract f i sidky and m atif mishref in 1990 introduced the concepts of divisible and pure fuzzy subgroups and proved some of their properties in this paper we further prove the following results if f g g is an isomorphism of groups and a is a divisible pure fuzzy subgroup of under min then f 1 a is a divisible pure fuzzy subgroup of g if b is a fuzzy1 subgroup of divisible subgroup h of g then there exists a subgroup h ofg and a fuzzy subgroup b of h such that g h h and a b b is a fuzzy subgroup of g if g is a divisible cyclic group then g is a finite group if a is a fuzzy subgroup of divisible cyclic group then a is trivial consider group g g1 g2 gm with gi a divisible cyclic subgroup of g i 1 2 m and suppose a is a divisible pure fuzzy subgroup of g under min then a is trivial

model c critical dynamics of disordered magnets the critical dynamics of model c in the presence of disorder is considered it is known that in the asymptotics a conserved secondary density decouples from the nonconserved order parameter for disordered systems however couplings between order parameter and secondary density cause considerable effects on non asymptotic critical properties here a general procedure for a renormalization group treatment is proposed already the one loop approximation gives a qualitatively correct picture of the diluted model c dynamical criticality a more quantitative description is achieved using two loop approximation in order to get reliable results resummation technique has to be applied

fuzzy normal subgroups and fuzzy quotients abstract in case of groups a mormal subgroup n of a group g can be defined with three equivalent approaches namely i as a kernel of some group homomorphism ii as a subgroup commuting with every element of g and iii as the subgroup n closed with respect to conjugates of elements of n in case of generalizations of this concept to fuzzy sets the elementwise third approach is found more suitable and hence is widely adopted by many authors in this paper we further study this concept of fuzzy subgroups and introduce fuzzy quotients called fuzzy quotient groups for all 0 1 two different definitions of these fuzzy quotients have been given which are shown to lead to isomorphic structures we also study the direct products of fuzzy normal subgroups min product as per the terminology of sherwood 1983 and the problem of writing a fuzzy normal subgroups of a direct product of some groups as a direct product of certain fuzzy normal subgroups has been discussed in detail

fuzzy ideals on a distributive lattice abstract we investigate the relationship between fuzzy ideals and fuzzy congruences on a distributive lattice and obtain that the lattice of fuzzy ideals is isomorphic to the lattice of fuzzy congruence on a generalized boolean algebra finally consider the products of fuzzy ideals

universality and criticality of a second order granular solid liquid like phase transition the authors experimentally study a vibrating granular layer that shows a transition between a disordered liquidlike phase and a phase with ordered crystalline clusters they study the properties of this nonequilibrium phase transition and find evidence for universality in the critical exponents

the fuzzy normal subgroup using the concept of fuzzy spaces we define the fuzzy normal subgroup in a fuzzy group its relation with the classical fuzzy normal subgroup is studied

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

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

fuzzy cosets and cyclic and abelian fuzzy subgroups abstract here we give some properties of fuzzy cosets normal fuzzy subgroups and s fuzzy subgroups also we introduce the notions of cyclic abelian fuzzy subgroups and prove some of their properties

some properties on fuzzy subgroups abstract in this paper the concept of homologous fuzzy subgroups of a group g is introduced and some properties on homologous fuzzy subgroups are obtained on the basis of bhattacharya and mukherjee inform sci 41 1987 77 91 and zhang and zou j fuzzy math 1 1993 571 585 the investigation of fuzzy centralizers fuzzy normalizers and fuzzy abelian subgroups is continued

two loop field theory and nonasymptotic properties of the dynamical model for the lambda transition in 3he 4he mixtures model f introduced by siggia and nelson phys rev b 15 1427 1977 describes the critical dynamics of 3he 4he mixtures near the superfluid transition using the minimal subtraction scheme this model is renormalized within dynamical field theory the dynamic zeta functions needed for the nonasymptotic flow properties are presented in two loop order the fixed points are discussed and the stable fixed points are identified the transition to limiting models contained in model f is shown analytically by performing the corresponding limits and numerically by calculating the nonlinear flow these results are the basis for further experimental comparison of the transport coefficents in 3he 4he mixtures at higher concentrations including the tricritical point

a characterization of fuzzy subgroups of some abelian groups abstract we introduce the notion of fuzzy p subgroups and characterize fuzzy subgroups of torsion groups and cyclic groups by their minimal fuzzy p subgroups and minimal fuzzy p subgroups

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

orders of fuzzy subgroups and fuzzy p subgroups abstract in this paper we introduce the notion of orders of fuzzy subgroups and the notion of fuzzy p subgroups by using the notion of fuzzy orders of elements and investigate some properties of fuzzy subgroups

fuzzy algebraic systems i direct products abstract first we introduce the concept of inner operational algebraic systems and fuzzy inner operational algebraic systems and so on after that we define the direct product of fuzzy algebraic systems and study its properties

critical dynamics a field theoretical approach we review the progress made in dynamic bulk critical behaviour in equilibrium in the last 25 years since the review of halperin and hohenberg we unify the presentation of the theoretical background by restricting ourselves to the field theoretic renormalization group method the main results obtained in the different universality classes are presented this contains the critical dynamics near the gas liquid transition in pure fluids model h the plait point and consolute point in mixtures model h the superfluid transition in 4 he model f and 4 he 3 he mixtures model f the curie point model j and neel point model g in heisenberg magnets and the superconducting transition in comparison with experimental results it became clear that in most cases one has to consider apart from the universal asymptotic critical behaviour also the non universal effective behaviour either because it turned out to be inevitable due to a small dynamical transient exponent inhibiting the system to reach the asymptotics e g at the superfluid transition or because one is interested in the region further away from the phase transition like in pure fluids and mixtures at their gas liquid or demixing transition the calculation of the critical dynamics is adequate in most cases only in two loop order we review these results and present the solution to unreasonable features found for some models thus we consider model c where relaxational and diffusive dynamics are coupled and the scaling properties and the limit to a purely relaxational model model a have not been understood in general for models where the order parameter couples to other conserved densities time scale ratios between the kinetic coefficients of the order parameter and the conserved densities play an important role their fixed point values and the approach to the fixed point are changed considerably in two loop order compared to their values in one loop order these considerations are relevant for the explanation of the dynamical critical shape functions of systems such as superfluid helium model f and the isotropic antiferromagnet model g as far as possible the comparison of results obtained by the renormalization group theory with numerical simulations has been made

semidirect products of fuzzy subgroups abstract the semidirect product of two groups is an important construction in group theory in this paper we define the semidirect product of fuzzy subgroups and give conditions for it to be a fuzzy subgroup this extends the work of h sherwood on direct products of fuzzy subgroups we then give an example where a fuzzy subgroup of a semidirect product is a semidirect product of fuzzy subgroups

direct products and isomorphism of fuzzy subgroups abstract the concepts of internal direct product and external direct product of fuzzy subgroups of a group are established as well as that of fuzzy isomorphism of fuzzy subgroups of possibly different groups it is shown that the internal direct product of two fuzzy subgroups of a group is isomorphic to their external direct product the fuzzy counterparts of the first and third isomorphism theorems are also proved

a new approach to fuzzy groupoids abstract we establish a new approach to fuzzy groupoids a concept of fuzzy binary operation is introduced in terms of the concepts of fuzzy cartesian product and fuzzy function introduced by the authors in a foregoing paper having defined a fuzzy binary operation the concepts of fuzzy groupoid subgroupoid homomorphism etc are introduced and investigated a theory of fuzzy groupoids is built up this approach is both intrinsic and more general than the well known current approach

fuzzy subgroups as products we find necessary and sufficient conditions for a fuzzy subgroup of a cartesian product of groups to be a cartesian product of fuzzy subgroups

divisible and pure fuzzy subgroups abstract as a continuation to the study of fuzzy subgroups which was given by a rosenfeld s sessa p s das h sherwood and others we introduce the concepts of divisible and pure fuzzy subgroups and prove some of their properties

divisible tl subgroups and pure tl subgroups abstract as a continuation of the study of divisible and pure fuzzy subgroups see sidky and mishref 1990 we introduce the concepts of divisible tl subgroups and pure tl subgroups of an additive group where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l and show some of their properties

products of fuzzy subgroups fuzzy subgroups are different from ordinary subgroups in that one cannot tell with certainty which group elements belong and which do not of course this requires an appropriate modification of the closure property which takes the form of an inequality in this paper a study of products of fuzzy subgroups is begun some results are expected the product of fuzzy subgroups is a fuzzy subgroup products with the same but permuted factors are isomorphic and there is a natural isomorphism from any factor into the product functions called t norms are used to construct products of fuzzy subgroups different t norms yielding different products since a fuzzy subgroup must satisfy an inequality generalizing closure and the strength of that inequality is important some results relate the t norm used in forming the product to the strength of the ensuing inequality when can complicated fuzzy subgroups be expressed as products of simple ones this question is addressed for fuzzy subgroups of finite abelian groups

critical dynamics of stochastic models with energy conservation model c we calculate the field theoretic functions of the generalized dynamical model c in which a conserved secondary density is coupled to a nonconserved complex order parameter in two loop order we show that the fixed points in this extended model are equal to the fixed points obtained in model c with a real order parameter which has been introduced by halperin hohenberg and ma our results correct long standing errors in the field theoretic functions in model c published by several authors leading also to different fixed point values w for the ratio of the two time scales involved the stability regions of the fixed points which remained partially unclear considered in a phase diagram whose axes are the spatial dimension d and number of order parameter components n are now clarified especially an anomalous region found by previous authors in which the scaling properties remained unsolved does not exist there are only two regions one with a finite fixed point w where the dynamical exponent z of the order parameter is z 2 alpha nu and another region where w 0 and z is equal to the model a value

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

fuzzy vector spaces under triangular norms abstract the object of this paper is to redefine fuzzy subspaces using the notion of a t norm and to obtain several results some of which are generalisations of the results of katsaras and liu 3