interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

equational characterization of all varieties of mv algebras abstract it is known that all subvarieties of mv algebras are finitely axiomatizable in the literature one can find equational characterizations of certain subvarieties such as mv n algebras in this paper we write down equational bases for all mv varieties and prove a representation theorem for each subvariety

on the entropy of dynamical systems in product mv algebras recently the so called product mv algebras have been introduced and the entropy of partitions in these algebras have been studied in this paper the previous results are applied to dynamical systems

bases of admissible rules of proper axiomatic extensions of ukasiewicz logic in this paper we give a base of admissible rules for every proper axiomatic extension of the infinite valued ukasiewicz logic we first prove that single conclusion admissible rules of any proper axiomatic extension are finitely based the proof strongly relies on the characterization of least v quasivarieties given in 11

on injectivity of semimodules over additively idempotent division semirings and chain mv semirings abstract in this paper we give a characterization of injective semimodules over additively idempotent semirings consequently we provide a complete description of injective semimodules over the semifield of tropical integers and give an explicit construction of the injective hulls of semimodules over chain division semirings we also give a criterion for self injective mv semirings with an atomic boolean center and describe the structure of finitely generated injective semimodules over finite mv semirings as well as we show that every complete mv semiring with an atomic boolean center is an exact semiring which is defined by a hahn banach type separation property on semimodules arising in the tropical case from the phenomenon of tropical matrix duality moreover we show that complete boolean algebras are precisely the mv semirings in which every principal ideal is injective

hulls of ordered algebras projectability strong projectability and lateral completeness abstract there has been compelling evidence during the past decade that lattice ordered groups l groups play a far more significant role in the study of algebras of logic than it had been previously anticipated their key role has emerged on two fronts first a number of research articles have established that some of the most prominent classes of algebras of logic may be viewed as l groups with a modal operator second and perhaps more importantly recent research has demonstrated that the foundations of the conrad program for l groups can be profitably extended to a much wider class of algebras namely the variety of e cyclic residuated lattices that is residuated lattices that satisfy the identity x e e x here the term conrad program refers to paul conrad s approach to the study of l groups that analyzes the structure of individual or classes of l groups by primarily focusing on their lattices of convex l subgroups the present article building on the aforementioned works studies existence and uniqueness of the laterally complete projectable and strongly projectable hulls of e cyclic residuated lattices while these hulls first made their appearance in the context of functional analysis and in particular the theory of riesz spaces their introduction into the study of algebras of logic adds new tools and techniques in the area and opens up possibilities for a deep exploration of their logical counterparts

pseudo bck algebras as partial algebras it is well known that the representation of several classes of residuated lattices involves lattice ordered groups an often applicable method to determine the representing group or groups from a residuated lattice is based on partial algebras the monoidal operation is restricted to those pairs that fulfil a certain extremality condition and else left undefined the subsequent construction applied to the partial algebra is easy transparent and leads directly to the structure needed for representation in this paper we consider subreducts of residuated lattices the monoidal and the meet operation being dropped the resulting algebras are pseudo bck semilattices assuming divisibility we can pass on to partial algebras also in this case to reconstruct the underlying group structure from this partial algebra if applicable is again straightforward we demonstrate the elegance of this method for two classes of pseudo bck semilattices semilinear divisible pseudo bck algebras and cone algebras

amalgamation and interpolation in ordered algebras the first part of this paper provides a comprehensive and self contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations in particular proofs are given of known equivalences between the amalgamation property and the robinson property the congruence extension property and the extension property and the flat amalgamation property and the deductive interpolation property as well as various dependencies between these properties these relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice ordered abelian groups and mv algebras and to determine important subvarieties of residuated lattices where these properties hold or fail in particular a full description is given of all subvarieties of commutative gmv algebras possessing the amalgamation property

unified graph based multi fluid model for gas liquid pipeline flows we present a novel model of transient multiphase flow for gas liquid mixtures in long pipelines the study develops a general flexible formulation of a one dimensional flow for complex multiphase mixtures in the presence of slip and mass exchange multi fluid and drift flux approaches are combined the multi fluid model governs the momentum balance for the fluids and drift flux correlations are used for modelling of the slip between individual components a tree like graph is introduced to describe the hierarchy of fluids and components within the mixture the numerical implementation for an arbitrary number of components is based on the extension of the semi implicit method for pressure linked equations imbalances of equations are selected as criteria for iteration convergence specific corrections are discussed including those proposed for the equilibrium gas release model

measures states and de finetti maps on pseudo bck algebras in this paper we extend the notions of states and measures presented in dvurecenskij and pulmannova 2000 12 to the case of pseudo bck algebras and study similar properties we prove that under some conditions the notion of a state in the sense of dvurecenskij and pulmannova 2000 12 coincides with the bosbach state and we extend to the case of pseudo bck algebras some results proved by kuhr only for pseudo bck semilattices we characterize extremal states and show that the quotient pseudo bck algebra over the kernel of a measure can be embedded into the negative cone of an archimedean group additionally we introduce a borel state and using results by kuhr and mundici 2007 28 we prove a relationship between de finetti maps bosbach states and borel states

analysis of iterative methods for the steady and unsteady stokes problem application to spectral element discretizations a new and detailed analysis of the basic uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady stokes operator is presented the paper focuses on the following new aspects explicit construction of the uzawa pressure operator spectrum for a semiperiodic model problem general relationship of the convergence rate of the uzawa procedure to classical inf sup discretization analysis and application of the method to high order variational discretization

topological characterization of filter topological mv algebras abstract motivated by the study of c topology on lattice ordered groups luan and yang introduced the concept of filter topology on mv algebras in a recent paper in order to have a better perception of this concept we study some basic facts and notable examples including the standard mv algebra and chang s algebra in this paper using the fact that an isomorphism between mv algebras admits a topological isomorphism between filter topological mv algebras we show that every filter topology on a finite linearly ordered finite simple mv algebra is discrete in addition we completely describe the shape of open sets in filter topology generated by a proper filter further the description is applied to present the basic topological properties of a large class of filter topologies as an application we characterize an algebraic property of mv algebras an mv algebra is bipartite if and only if it has a proper filter which generates a filter topology with exactly four open sets

every state on semisimple mv algebra is integral integral representation theorem will be established for finitely additive probability measures states on semisimple mv algebras this result generalizes the well known theorem of butnariu and klement in case of order continuous states on tribes of fuzzy sets precisely it will be demonstrated that every state on a separating clan of continuous fuzzy sets arises as an integral with respect to a unique borel probability measure the key technique leading to this result exploits the geometrical topological properties of the state space the set of all states on every mv algebra forms a bauer simplex

representable pseudo bck algebras and integral residuated lattices abstract pseudo bck algebras arise as the 1 subreducts of integral residuated lattices in this note we characterize pseudo bck algebras that are subdirect products of linearly ordered pseudo bck algebras

generalized fuzzy connectives onmv algebras w x the theory of mv algebras developed by c c chang 8 9 first w x appeared in 1958 several years later zadeh 14 published his fundamental paper on fuzzy set theory the two theories had independent motivations mv algebras were developed to provide an algebraic proof of the completeness theorem for ukasiewicz infinite valued propositional logic fuzzy set theory was proposed to provide a mathematical basis for sets where in reality set membership was vague the logic of ukasiewicz includes in some sense two valued classical logic fuzzy set theory includes the usual two valued characteristic functions thus both theories are extensions of classical logic both of the above theories use as a basis of interpretation the real unit w x w x interval 0 1 the basic mv algebraic operations on 0 1 are a b s u min 1 a q b a b s max 0 a q b y 1 and a s 1 y a the basic fuzzy w x theoretic operations on 0 1 suggested by zadeh are a k b s max a b u a n b s min a b and a s 1 y a now the operations k and n can be defined in terms of and u thus the ukasiewicz operations are more general and include the basic fuzzy operations by pointwise extension we obtain given an arbitrary set x b two w x x u algebraic structures on 0 1 say a determined by and a 1 2 determined by k n a is an mv algebra and is often referred to as 1 the bold algebra of fuzzy subsets of x a is the basic algebra of fuzzy 2 subsets of x by the remark above that k n can be defined in terms of u we see that a is some type of substructure of a 2 1

least v quasivarieties of mv algebras this paper is a contribution to the study of the lattice of all quasivarieties of mv algebras given a variety v of mv algebras we say that a quasivariety is a v quasivariety provided that it generates v as a variety it turns out that every variety has a least v quasivariety denoted by q v moreover it is generated as a quasivariety by its free algebra over an infinite set of generators we obtain a komori s type characterization of q v for every proper subvariety of mv algebras we investigate the order structure of the poset of least v quasivarieties and we find all minimal quasivarieties among all quasivarieties of mv algebras different from the class of boolean algebras finally we make some remarks on the logical interpretation of least v quasivarieties of mv algebras as structurally complete extensions of the infinite valued ukasiewicz logic

on limit theorems in fuzzy quantum spaces two kinds of fuzzy connectives are used for constructing two models of quantum mechanics in the framework some versions of the weak law of large numbers and the central limit theorem are presented

extensions for af algebras and dimension groups let a c be approximately finite dimensional af c algebras with a nonunital and c unital suppose that either i a is the algebra of compact operators or ii both a c are simple the classification of extensions of a by c is studied here by means of elliott s dimension groups in case i the weak ext group of c is shown to be extz ko c z and the strong ext group is an extension of a cyclic group by the weak ext group conditions under which either ext group is trivial are determined in case ii there is an unnatural and complicated group structure on the classes of extensions when a has only finitely many pure finite traces and somewhat more generally our motivating theme is to consider extensions of c algebras by other than the algebra of compact operators because af algebras are describable in terms of partially ordered groups they seem particularly suitable for this extension theory as the ordered groups arising from simple af algebras are fairly well understood it turns out that one can solve completely the problem of classifying simple by simple af algebras when the finite trace space of the bottom af algebra has finite dimensional dual in the course of doing this we establish formulae for the usual strong and weak ext groups of af algebras our homological approach to this differs from the computational viewpoint of pimsner and popa 14 15 we consider short exact sequences extensions of c algebras a b c with b an af algebra there is a translation to extensions within a class of partially ordered abelian groups and distinguished subset known as dimension groups with interval via the functor ko0 this translation is reversible owing to a recent result of l brown that an extension of an af algebra by an af algebra is af so all c extensions are represented as dimension group extensions with the appropriate notion of equivalence extending strong equivalence as defined in 3 p 268 when a is the algebra of compact operators on a separable hilbert space the equivalence classes admit a limited additive operation often forming a disjoint union of groups a single group results if for example both a and c are simple with a unitless but not necessarily stable 1 deals with the appropriate definitions of extensions dimension groups equivalence and the translation between af algebras and dimension groups much of this is well known in the second section it is shown that if a is simple stable and c is received by the editors december 11 1979 and in revised form march 25 1981 1980 mathematics subject classification primary 46l35 secondary 54a22 16a54 16a56 06f20 supported in part by an operating grant from nserc of canada d1982 american mathematical society 0002 9947 82 0000 1 059 09 75

loomis sikorski representation of monotone σ complete effect algebras we show that monotone s complete effect algebras with the riesz decomposition property are s homomorphic images of effect tribes with the riesz decomposition property which are effect algebras of fuzzy sets closed under pointwise limits of nondecreasing fuzzy sets

algebraic structures in fuzzy logic abstract common features in various fuzzy logical systems are investigated it turns out that adjoint couples and residuated lattices are very often present though not always explicitly expressed some minor new results are also proved

some properties of pseudo bck and pseudo bci algebras abstract pseudo bci algebras generalize both bci algebras and pseudo bck algebras which are a non commutative generalization of bck algebras in this paper following 37 we show that pseudo bci algebras are the residuation subreducts of semi integral residuated po monoids and characterize those pseudo bci algebras which are direct products of pseudo bck algebras and groups regarded as pseudo bci algebras we also show that the quasivariety of pseudo bci algebras is relatively congruence modular in fact we prove that this holds true for all relatively point regular quasivarieties which are relatively ideal determined in the sense that the kernels of relative congruences can be described by means of ideal terms

an asymptotic finite element method for improvement of solutions of boundary layer problems a scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented the proposed scheme improves the error bounds of the standard galerkin finite element scheme by a factor of o en 1 where e is the small parameter andn is the order of the asymptotic approximation numerical results for linear second order o d e s are given and are compared with several other schemes

generalized mv algebras we generalize the notion of an mv algebra in the context of residuated lattices to include noncommutative and unbounded structures we investigate a number of their properties and prove that they can be obtained from lattice ordered groups via a truncation construction that generalizes the chang mundici functor this correspondence extends to a categorical equivalence that generalizes the ones established by d mundici and a dvurey the decidability of the equational theory of the variety of generalized mv algebras follows from our analysis

the conrad program from l groups to algebras of logic abstract a number of research articles have established the significant role of lattice ordered groups l groups in logic the fact that underpins these studies is the realization that important algebras of logic may be viewed as l groups with a modal operator these connections are just the tip of the iceberg the purpose of the present article is to lay the groundwork for and provide significant initial contributions to the development of a conrad type approach to the study of algebras of logic the term conrad program refers to paul conrad s approach to the study of l groups which analyzes the structure of individual or classes of l groups by primarily using strictly lattice theoretic properties of their lattices of convex l subgroups the present article demonstrates that large parts of the conrad program can be profitably extended in the setting of e cyclic residuated lattices that is residuated lattices that satisfy the identity x e e x an indirect benefit of this work is the introduction of new tools and techniques in the study of algebras of logic and the enhanced role of the lattice of convex subalgebras of a residuated lattice

a variational bound nip element method for geometrically stiff problems application to thermal composites and porous media geometrically stiff problems problems which exhibit disparate length scales geometric in origin arise frequently in fluid mechanics and heat transfer perhaps most prevalently in the analysis of multicomponent media in this paper we present a hybrid analytico computational approach to the treatment of geometrically stiff problems for which the quantity of interest can be expressed as the extremum of a functional more precisely we consider in depth the effective conductivity of random thermal composites and briefly the permeability of random porous media the approach proceeds by an inner outer decomposition in which analytical approximations in inner nip regions are folded into modified outer problems defined over geometrically more homogeneous domains the technique considerably mitigates the numerical difficulties associated with geometric stiffness by reduced degrees of freedom improved conditioning less stringent mesh generation requirements and better parallel load balancing while simultaneously providing rigorous upper and lower bounds for the quantity of interest furthermore the method enjoys certain convergence properties the upper lower bound gap can be rendered systematically smaller by decreasing the extent of the inner nip regions we first describe a series of bound procedures and associated modified outer weak forms we next discuss finite element implementation of the outer problem on message passing multicomputers here the intel ipsc 860 hypercube and finally we present several illustrative examples

stone duality above dimension zero axiomatising the algebraic theory of c x abstract it has been known since the work of duskin and pelletier four decades ago that k op the opposite of the category of compact hausdorff spaces and continuous maps is monadic over the category of sets it follows that k op is equivalent to a possibly infinitary variety of algebras in the sense of slominski and linton isbell showed in 1982 that the lawvere linton algebraic theory of can be generated using a finite number of finitary operations together with a single operation of countably infinite arity in 1983 banaschewski and rosick independently proved a conjecture of bankston establishing a strong negative result on the axiomatisability of k op in particular is not a finitary variety isbell s result is best possible the problem of axiomatising by equations has remained open using the theory of chang s mv algebras as a key tool along with isbell s fundamental insight on the semantic nature of the infinitary operation we provide a finite axiomatisation of

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

mathematical structure of the black oil model for petroleum reservoir simulation this model incorporates compressibility and general mass transfer between phases it consists of the conditions of thermodynamic equilibrium an equation of state for the volume balance between the fluidand the rock void darcy s law for the volumetric flow rates and component conservation equations these relations are manipulated to form a pressure equation and a modified system of component conservation equations it is shown that the pressure equation is parabolic and that in the absence of diffusive forces such as capillary pressure and mixing the component conservation equations are hyperbolic subject to technical conditions on the relative permeabilities this sequential formulation of the flow equations forms types of wave structures that occur for the system

on the geometric theory of local mv algebras abstract we investigate the geometric theory of local mv algebras and its quotients axiomatizing the local mv algebras in a given proper variety of mv algebras we show that whilst the theory of local mv algebras is not of presheaf type each of these quotients is a theory of presheaf type which is morita equivalent to an expansion of the theory of lattice ordered abelian groups di nola lettieri s equivalence is recovered from the morita equivalence for the quotient axiomatizing the local mv algebras in chang s variety that is the perfect mv algebras we establish along the way a number of results of independent interest including a constructive treatment of the radical for mv algebras in a fixed proper variety of mv algebras and a representation theorem for the finitely presentable algebras in such a variety as finite products of local mv algebras

closure operations on mv algebras abstract closure operations on posets have been investigated and applied extensively to lattices of congruences of various algebraic structures in this paper we initiate the study of closure operations on mv algebras and star operations on mv modules the connections between closure star operations studied here and those of semirings as well as those of lattice ordered rings are also investigated we provide several examples of these closure operations and star operations and also study some of their main properties

coproductmv algebras nonstandard reals and riesz spaces abstract up to categorical equivalence mv algebras are unit intervals of abelian lattice ordered groups for short l groups with strong unit while the property of being a strong unit is not even definable in first order logic mv algebras are definable by a few simple equations accordingly such notions as ideals and coproducts are definable for anymv algebraaas particular cases of the general algebraic notions the radical rad ais the intersection of all maximal ideals ofa anmv algebraais said to be local iff it has a unique maximal ideal then by hoelder s theorem the quotienta rad ais isomorphic to a subalgebra of the real unit interval 0 1 using nonstandard real numbers we give a concrete representation of those totally orderedmv algebrasawhich are isomorphic to the coproduct ofa rad aand rad a the latter denoting the subalgebra ofagenerated by its radical as an application using several categorical equivalences we describe themv algebraic counterparts of riesz spaces also known as vector lattices