results on the use of category theory for the study of lattice valued finite state machines in this paper we introduce the concepts of category of lattice valued finite state machines category of quasi lattice valued transformation semigroups category of quasi lattice valued transformation monoids category of lattice valued transformation semigroups category of lattice valued transformation monoids and six pairs of functors each pair of functors have the adjoint property we discuss the relation between the categories with functors and give the adjoint theorems and relation theorems

asymptotic behavior of large solutions to p laplacian of bieberbach rademacher type abstract by the karamata regular variation theory and the method of lower and upper solutions we establish the asymptotic behavior of boundary blow up solutions of the quasilinear elliptic equation div u p 2 u b x f u in a bounded r n subject to the singular boundary condition u x where the weight b x is non negative and non trivial in which may be vanishing on the boundary or go to unbounded the nonlinear term f is a varying function at infinity whose variation at infinity is not regular

fuzzy recognizers and recognizable sets in this paper the concepts of fuzzy recognizers and recognizable sets are studied and their relationship with various products of fuzzy finite state machines is established the tools necessary for such study are developed the ideas of reversal inverse image accessible part coaccessible part trim part regarding fuzzy recognizers are introduced and their properties are discussed

random walks exterior to a rectangle the author shows how to simulate random walks terminating on the periphery of a rectangle both in the continuum and on a square lattice the method is error free in principle except for a negligible bias arising from the rejection of very long walks the average machine time would be o 1 step in the modified procedure this method may be useful in exploring the distinction between the continuum and the lattice in diffusion limited aggregation

asymptotic behavior of entire large solutions to semilinear elliptic equations abstract in this paper by using karamata regular variation theory we study the exact asymptotic behavior of entire large solutions to u b x f u x r n n 3 where b c r n is nonnegative and nontrivial in r n f c 0 is positive and non decreasing on 0 which satisfies keller osserman condition and is rapidly varying or regularly varying at infinity with index 1

clinical monitoring with fuzzy automata abstract in this paper a framework for an intelligent bedside monitor is presented the monitor derives an abstraction of the current status of a patient by performing fuzzy state transitions on pre processed input continuously supplied by clinical instrumentation so far an implementation called diamon 1 has been used for off line evaluation of data of patients suffering from the adult respiratory distress syndrome ards

algebraic properties of l fuzzy finite automata fuzzy automata theory on lattice ordered monoids was introduced by li and pedrycz dropping the distributive laws fuzzy finite automata l ffas for short based on a more generalized structure l named a po monoid are presented and investigated from the view of algebra in this paper the notions of strong successor and source operators fuzzy successor and source operators which are shown to be closure operators on certain conditions are introduced and discussed in detail using the weak primary submachines a unique decomposition theorem of a fuzzy finite automaton based on a lattice ordered monoid is obtained taking l as a quantale fuzzy subsystems are proved to be the same as fuzzy submachines of an l ffa in particular intrinsic connections between algebraic properties of l and properties of some operators of an l ffa are discovered it is shown that the join preserving property of fuzzy successor and source operators can be fully characterized by the right and left distributive laws respectively and the idempotence of successor operator can be characterized equivalently by the nonexistence of zero divisors when l is a lattice ordered monoid

a second order estimate for blow up solutions of elliptic equations abstract we investigate second term asymptotic behavior of boundary blow up solutions to the problems u b x f u x subject to the singular boundary condition u x in a bounded smooth domain r n b x is a non negative weight function the nonlinearly f is regularly varying at infinity with index 1 that is lim u f u f u for every 0 and the mapping f u u is increasing on 0 the main results show how the mean curvature of the boundary appears in the asymptotic expansion of the solution u x our analysis relies on suitable upper and lower solutions and the karamata regular variation theory

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 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

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

boundary blow up in nonlinear elliptic equations of bieberbach rademacher type the research of the first author was carried out at victoria university melbourne with the support of the australian government through detya the second author has been supported by grant 2 cex06 11 18 2006

on fuzzy ideals and fuzzy quotient rings of a ring abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and give the notion of fuzzy nilpotent ideals we give also a characterization of semiprime rings in terms of fuzzy ideals

asymptotic estimates of boundary blow up solutions to the infinity laplace equations abstract in this paper we study the asymptotic behavior of boundary blow up solutions to the equation u b x f u in where is the laplacian the nonlinearity f is a positive increasing function in 0 and the weighted function b c is positive in and may vanish on the boundary we first establish the exact boundary blow up estimates with the first expansion when f is regularly varying at infinity with index p 3 and the weighted function b is controlled on the boundary in some manner furthermore for the case of f s s p 1 c g s with the function g normalized regularly varying with index q 0 we obtain the second expansion of solutions near the boundary it is interesting that the second term in the asymptotic expansion of boundary blow up solutions to the infinity laplace equation is independent of the geometry of the domain quite different from the boundary blow up problems involving the classical laplacian

products of mealy type fuzzy finite state machines we introduce seven ways of constructing products for mealy type fuzzy finite state machines as well as the concept of covering the properties of transition functions and output functions are discussed furthermore we investigate the covering properties and mutual relationship with regard to these products we also prove that the covering relationship holds in the product of factor machines

on generalized characteristic fuzzy subgroups of a finite group abstract in 1991 asaad 2 suggested the following two questions i what can be said about the structure of a fuzzy subgroup a of a finite group g when information is known about the structure of g ii what can be said about the structure of group g when information is known about the structure of a fuzzy subgroup a of g the purpose of this paper is to continue the investigation of the above questions

products of t generalized state machines and t generalized transformation semigroups abstract we introduce the concepts of t generalized state machines t generalized transformation semigroups and coverings and direct products of t generalized state machines and t generalized transformation semigroups and we investigate some of algebraic properties of them

the second order expansion of boundary blow up solutions for infinity laplacian equations abstract in this paper by using karamata regular variation theory and a perturbed argument we study the second order expansion of viscosity solutions to boundary blow up elliptic problem u b x f u x u where is a bounded domain with c 2 boundary in r n b c is non negative and non trivial in f c 1 0 is a normalized regularly varying function at infinity with index 3

the structure of two dimensional witten sander aggregates a relatively large number 102 103 of reasonably large about 105 particles or sites two dimensional witten sander aggregates are simulated using new algorithms this enables the reduction of statistical errors by an order of magnitude and provides an opportunity to determine some new quantities describing in more detail the structure of witten sander clusters a quantitate description of the distortion of large lattice based witten sander clusters into a diamond like shape is provided the orientational correlation in the bond directions for off lattice witten sander clusters is also measured this quantity has a power law dependence on distance with an exponent of about 0 37

on relationships among fuzzy approximation operators fuzzy topology and fuzzy automata the fuzzy approximation operator associated with an approximation space x r turns out to be a saturated kuratowski fuzzy closure operator on x precisely when the relation r on x is reflexive and transitive it is shown that all the level topologies of the fuzzy topology so obtained on x coincide these observations are then applied to fuzzy automata

fuzzy cosets and fuzzy normal subgroups abstract in this paper besides generalizing some of the results of mukherjee and bhattacharya 9 we investigate conditions under which a homomorphic image of a fuzzy normal subgroup is fuzzy normal we also prove that a fuzzy subgroup of order p n 1 of a group of order p n is a fuzzy normal subgroup if p is a prime

on category of l fuzzy automata coalgebras and dialgebras abstract this paper is towards the study of l fuzzy automata from the categorical point of view where l is a complete residuated lattice we introduce a functor having both the left right adjoint from the category of l fuzzy semiautomata lfsa to the category lftcrl a category of complete residuated lattices corresponding to l fuzzy semiautomata the l fuzzy response map of an l fuzzy automaton leads us to provide a characterization of an l fuzzy regular language interestingly we show that the category lfsa is a category of t 1 coalgebras t 2 t 3 dialgebras moreover we establish a relationship between the category of t 1 coalgebras and the category of t 2 t 3 dialgebras

blow up rates of large solutions for elliptic equations in this paper we mainly study the boundary behavior of solutions to boundary blow up elliptic problems for more general nonlinearities f which may be rapidly varying at infinity u b x f u x u where is a bounded domain with smooth boundary in rn and b c which is positive in and may be vanishing on the boundary and rapidly varying near the boundary further when f s sp f1 s for s sufficiently large where p 1 and f1 is normalized regularly varying at infinity with index p1 0 p we show the influence of the geometry of on the boundary behavior for solutions to the problem we also give the existence and uniqueness of solutions

decompositions of t generalized transformation semigroups we introduce several decompositions of t generalized transformation semigroups and investigate some of algebraic properties of them

on subsystems of a fuzzy finite state machine abstract in this paper we study subsystems and strong subsystems of a fuzzy finite state machine the ideas of cyclic subsystem and simple strong subsystem are introduced and their basic properties are examined

asymptotic boundary estimates to infinity laplace equations with γ varying nonlinearity abstract in a previous paper of the authors wang et al 2014 40 the asymptotic estimates of boundary blow up solutions were established to the infinity laplace equation u b x f u in r n with the nonlinearity 0 f c 0 regularly varying at and the weighted function b c positive in and vanishing on the boundary the present paper gives a further investigation on the asymptotic behavior of boundary blow up solutions to the same equation by assuming f to be varying note that a varying function grows faster than any regularly varying function we first quantitatively determine the boundary blow up estimates with the first expansion relying on the decay rate of b near the boundary and the growth rate of f at infinity and further characterize these results via examples possessing various decay rates for b and growth rates for f in particular we pay attention to the second order estimates of boundary blow up solutions it was observed in our previous work that the second expansion of solutions to the infinity laplace equation is independent of the geometry of the domain quite different from the classical laplacian the second expansion obtained in this paper furthermore shows a substantial difference on the asymptotic behavior of boundary blow up solutions between the infinity laplacian and the classical laplacian

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

the lattices of fuzzy subgroups and fuzzy normal subgroups abstract here we discuss various types of sublattices of the lattice of fuzzy subgroups of a given group we prove that a special class of fuzzy normal subgroups constitutes a modular sublattice of the lattice of fuzzy subgroups

a fuzzy topology associated with a fuzzy finite state machine abstract given a fuzzy finite state machine m q a fuzzy closure operator is defined which induces a lowen type fuzzy topology in q the concepts of separation of fuzzy subsystems and connectedness of fuzzy finite state machines are developed some results on connectedness and weak connectedness of fuzzy subsystems are obtained characterizations of these concepts in terms of the fuzzy topology are also obtained

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

the second expansion of large solutions for semilinear elliptic equations abstract in this paper we analyze the influence of the domain geometry in the second expansion of solutions to the boundary blow up elliptic problem u b x f u u 0 x u where is a bounded domain with c 4 smooth boundary in r n b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p p 1

on covering of products of fuzzy finite state machines in this paper we have given several ways of constructing products of fuzzy finite state machines and their mutual relationship through isomorphism and coverings products called direct sum and sum of fuzzy finite state machines are introduced some algebraic properties of these products are investigated it is proved that the wreath product of two fuzzy finite state machines covers their cascade products similar relationship holds in direct sum and sum of two fuzzy finite state machines an interesting distributive property of cascade product over the sum of fuzzy finite state machines in relation to covering of fuzzy finite state machine is established

random walks for on lattice dla simulations two efficient ways to accelerate on lattice dla simulations without introducing any bias are presented the first requires one dimensional tables but little arithmetic the second needs no tables but necessitates the evaluation of a few elementary functions

isomorphic fuzzy groups abstract we introduce an acceptable definition of isomorphic fuzzy groups which fulfils the basic requirements the fuzzy versions of the first and the second isomorphism theorems become immediate consequences the idea is applied to the sup min product of two fuzzy subgroups of a group as an indispensable tool the characterization of a fuzzy normal subgroup of a group by the so called open level subgroups is brought forth an isomorphism between the cartesian product and the sup min product of two fuzzy subgroups of a group is demonstrated

boundary behaviour for solutions of boundary blow up problems in a borderline case we investigate boundary blow up solutions of the equation u f u in a bounded domain rn under the condition that f t has a relatively slow growth as t goes to infinity we show how the mean curvature of the boundary appears in the asymptotic expansion of the solution u x in terms of the distance of x from

large solutions of elliptic semilinear equations in the borderline case an exhaustive and intrinsic point of view abstract we revisit the problem u f u in u x as x where r n n 1 is a bounded smooth domain and f is an increasing and continuous function in r with f 0 0 for which the keller osserman condition holds we study uniqueness of solutions extending known results about the boundary blow up behavior of solutions furthermore we obtain explicit representations for the second order terms in the explosive boundary expansion of solutions under intrinsic and direct assumptions our study is exhaustive including both ordinary and borderline cases providing new and sharp results

on some properties of fuzzy semiautomaton over a finite group abstract the notion of group semiautomata has been fuzzified the ideas of a fuzzy kernel and a fuzzy subsemiautomaton of a fuzzy semiautomaton over a finite group are introduced using the notion of fuzzy normal subgroup and fuzzy subgroup respectively some results concerning them are deduced

second order expansion for blowup solutions of semilinear elliptic problems abstract in this paper we mainly study the second order expansion of solutions to the elliptic problems u b x f u u 0 x u where is a bounded domain with a smooth boundary in r n n 2 b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p 1 our analysis is based on the sub supersolution method and karamata regular variation theory

problems for elliptic singular equations with a quadratic gradient term we investigate the homogeneous dirichlet problem for a class of second order elliptic partial differential equations with a quadratic gradient term and singular data in particular we study the asymptotic behaviour of the solution near the boundary under suitable assumptions on the growth of the coefficients of the equation

characterizations of fuzzy finite automata in this paper we establish some important concepts in fuzzy finite automata ffas with bifuzzy property and clarify their essential relationships first we present a number of basic definitions and properties in ffas we then define a bifuzzy family of subautomata bifuzzy source and successor operators as well as demonstrate the bifuzzy topological characterization of ffas also we clarify the relationships between our results and previous ones and thus derive a relation figure visualizing their connections afterwards we investigate further the bifuzzy separability retrievability and homomorphism fuzzy continuous mapping and open mapping are also incorporated in particular we prove a number of equivalent characterizations for these concepts and expound the relationships amongst them this also concludes that both the bifuzzy source and successor operators are fuzzy closure operators we discover that our investigation generalizes to some extent the algebraic fuzzy automata elaborated by malik mordeson and others finally the main results obtained are summarized the potential applications are indicated and a number of related problems for further study are addressed