a non hyponormal operator generating stieltjes moment sequences abstract a linear operator s in a complex hilbert space h for which the set d s of its c vectors is dense in h and s n f 2 n 0 is a stieltjes moment sequence for every f d s is said to generate stieltjes moment sequences it is shown that there exists a closed non hyponormal operator s which generates stieltjes moment sequences what is more d s is a core of any power s n of s this is established with the help of a weighted shift on a directed tree with one branching vertex the main tool in the construction comes from the theory of indeterminate stieltjes moment sequences as a consequence it is shown that there exists a non hyponormal composition operator in an l 2 space over a finite measure space which is injective paranormal and which generates stieltjes moment sequences the independence assertion of barry simon s theorem which parameterizes von neumann extensions of a closed real symmetric operator with deficiency indices 1 1 is shown to be false

unbounded subnormal weighted shifts on directed trees ii abstract a new method of verifying the subnormality of unbounded hilbert space operators based on an approximation technique is proposed diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established an approach to this issue via consistent systems of probability measures is invented the role played by determinate stieltjes moment sequences is elucidated lambert s characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi analytic vectors which is a new phenomenon in this area

the center of thin gaussian groups abstract thin gaussian groups are a natural generalization of spherical artin groups namely groups of fractions of monoids in which the existence of least common multiples is kept as an hypothesis but the relations between the generators are not supposed to necessarily be of coxeter type here we completely describe the center of thin gaussian groups by constructing a minimal generating set for the quasi center we deduce that every thin gaussian group is an iterated crossed product of thin gaussian groups with a cyclic center

aluthge transforms of weighted shifts on directed trees aluthge transform of a bounded operator is generalized to the case of unbounded one a formula for the aluthge transform of a weighted shift on a directed tree is established and it is used to construct an example of a hyponormal operator whose aluthge transform has trivial domain it is proven that such an example can be also constructed in the class of composition operators it is also shown that aluthge transform of a closed densely defined operator is not necessarily closable

associative monotonic operations in fuzzy set theory abstract the properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets on fuzzy numbers and on fuzzy probabilistic sets

reduced commutativity of moduli of operators abstract in this paper we investigate the question of when the equations a s a s a a s s s where s is a finite set of positive integers imply the quasinormality or normality of a in particular it is proved that if s p m m p n n p where p 1 and 2 m n then a is quasinormal moreover if a is invertible and s m n n m with m n then a is normal the case when s m m n and a n a n a a n is also discussed

artin groups of spherical type up to isomorphism we prove that two artin groups of spherical type are isomorphic if and only if their defining coxeter graphs are the same

cauchy like functional equations for uninorms continuous in 0 1 2 abstract commutativity is an important property in two step information merging procedure it is shown that the result obtained from the procedure should not depend on the order in which signal steps are performed in the case of a bisymmetric aggregation operator with the neutral element saminger et al have provided a full characterization of commutative n ary operator by means of unary distributive functions further characterizations of these unary distributive functions can be viewed as resolving a kind of the cauchy like equations f x y f x f y where f 0 1 0 1 is a monotone function is a bisymmetric aggregation operator with the neutral element in this paper we are still devoted to investigating and fully characterizing the cauchy like equation f u x y u f x f y where f 0 1 0 1 is an unknown function but not necessarily monotone u is a uninorm continuous in 0 1 2 these results show the key technology is how to find a transformation from this equation into several known cases moreover this equation has completely different and non monotone solutions in comparison with the obtained results

migrative uninorms and nullnorms over t norms and t conorms in this paper the notions of migrative uninorms and nullnorms over a fixed t norm t and over a fixed t conorm s are introduced and studied all cases when the uninorm u lies in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations of u and t and for all possible combinations of u and s a similar study is done for nullnorms

right l groups geometric garside groups and solutions of the quantum yang baxter equation abstract right lattice ordered groups are introduced and studied as a general framework for garside groups and related groups without a garside element every right l group g has a two sided partially ordered subgroup n g which generalizes the quasi centre of an artin tits group the group n g splits into copies of z if g is noetherian the positive cone of a right l group is described as a structure that is known from algebraic logic a pair of left and right self similar hoops for noetherian right l groups g modularity of the lattice structure is characterized in terms of an operation on the set x g of atoms it is proved that modular garside groups are equivalent to finite projective spaces with a non degenerate labelling a concept of duality for x g is introduced and applied in the distributive case this gives a one to one correspondence between noetherian right l groups with duality and non degenerate unitary set theoretic solutions of the quantum yang baxter equation the description of garside groups via garside germs is extended to right l groups which yields a one sided enhancement and a new proof of dvurecenskij s non commutative extension of mundici s correspondence between abelian l groups and mv algebras

on the structure of special classes of uninorms in this paper the concept of the reidemeister closure condition is adopted in order to characterize associativity of uninorms with a special attention paid to the class of representable uninorms thus conditions replacing the associativity requirement for such uninorms are given further the attention is focused on the uninorms where the underlying t norm and t conorm are idempotent or induce an involutive negator based on the aforementioned results the structure of these classes of uninorms is fully described

the language of geodesics for garside groups we prove that the language of all geodesics of any garside group with respect to the generating set of divisors of the garside element forms a regular language in particular the braid groups admit generating sets where the associated language of geodesics is regular

injectivity on the set of conjugacy classes of some monomorphisms between artin groups there are well known monomorphisms between the artin groups of finite type an bn cn and affine type a n 1 c n 1 the artin group a an is isomorphic to the n 1 strand braid group bn 1 and the other three artin groups are isomorphic to some subgroups of bn 1 the inclusions between these subgroups yield monomorphisms a bn a an a a n 1 a bn and a c n 1 a bn there are another type of monomorphisms a bd a amd 1 a bd a bmd and a bd a amd which are induced by isomorphisms between artin groups of type b and centralizers of periodic braids in this paper we show that the monomorphisms a bd a amd 1 a bd a bmd and a bd a amd induce injective functions on the set of conjugacy classes and that none of the monomorphisms a bn a an a a n 1 a bn and a c n 1 a bn does so

migrativity property for uninorms the migrative uninorms over a fixed uninorm with different neutral elements are presented all cases when both uninorms lay in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations the solutions obtained generalize the results where both uninorms have the same neutral elements

open problems from the 12th international conference on fuzzy set theory and its applications eighteen open problems posed during fsta 2014 liptovsk jan slovakia are presented these problems concern fuzzy logics fuzzy partitions copulas triangular norms and related aggregation functions some open problems concerning effect and mv algebras are also included

a generalization of the migrativity property of aggregation functions this paper brings a generalization of the migrativity property of aggregation functions suggested in earlier work of some of the present authors by imposing the a migrativity property of durante and sarkoci for all values of a instead of a single one replacing the algebraic product by an arbitrary aggregation function b naturally leads to the properties of a b migrativity and b migrativity this generalization establishes a link between migrativity and a particular case of aczel s general associativity equation already considered by cutello and montero as a recursive formula for aggregation following a basic investigation emphasis is put on aggregation functions that can be represented in terms of an additive generator more specifically strict t norms strict t conorms and representable uninorms

on migrativity property for uninorms recently u 0 migrative uninorms u were introduced and discussed where u and u 0 are two uninorms with neutral element e in this paper we will further study u 2 migrative uninorms u 1 where u 1 and u 2 are two uninorms with different neutral elements e 1 and e 2 respectively all cases when the uninorm u 1 and u 2 are in different families out of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations of u 1 and u 2

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

on properties of uninorms with underlying t norm and t conorm given as ordinal sums uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory this paper presents some properties of uninorm like operations for which the underlying operations are given by ordinal sums if the underlying operations of a uninorm are given by ordinal sums then the cartesian product of the union of two arbitrary intervals one in 0 e and the other in e 1 where e is the neutral element of the uninorm is a set closed under the uninorm when transposing such a cartesian product to the unit square one obtains a uninorm like operation as a result we have described the uninorm like operations for which the underlying operations are basic pseudo t norms and pseudo t conorms and one of them is idempotent

decomposition of garside groups and self similar l algebras abstract picantin s iterated crossed product representation of garside monoids is extended and reproved for a wide class of not necessarily noetherian partially ordered groups with a right invariant lattice structure it is shown that the tree like structure of such an iterated crossed product is equivalent to a partial cycle set closely related to a class of set theoretic solutions of the quantum yang baxter equation the decomposition of finite square free solutions is related to the crossed product representation of the corresponding structure group

ordinal sums of representable uninorms abstract we investigate properties of an ordinal sum of uninorms in the case that the summands are proper representable uninorms we show sufficient and necessary conditions for a uninorm to be an ordinal sum of representable uninorms an example is also included

unitary equivalence of operator valued multishifts abstract we systematically study various aspects of operator valued multishifts beginning with basic properties we show that the class of multishifts on the directed cartesian product of rooted directed trees is contained in that of operator valued multishifts further we establish circularity analyticity and wandering subspace property of these multishifts in the rest part of the paper we study the function theoretic behaviour of operator valued multishifts we determine the bounded point evaluation reproducing kernel structure and the unitary equivalence of operator valued multishifts with invertible operator weights in contrast with a result of lubin it appears that the set of all bounded point evaluations of an operator valued multishift may be properly contained in the joint point spectrum of the adjoint of underlying multishift

characterizations of uni nullnorms with continuous archimedean underlying t norms and t conorms abstract a uni nullnorm is a special case of 2 uninorms obtained by letting a uninorm and a nullnorm share the same underlying t conorm in this paper we give complete descriptions of uni nullnorms with continuous archimedean underlying t norms and t conorms

rotation invariant t norms the rotation invariance property revisited focusing on conjunctive left continuous increasing 0 1 2 0 1 functions t we redefine the rotation invariance property in terms of contour lines under the assumption of the existence of a neutral element email protected 0 1 this rotation invariance property requires some partial commutativity and associativity the functions that are rotation invariant w r t all of their contour lines are characterized

a solution to the cauchy dual subnormality problem for 2 isometries abstract the cauchy dual subnormality problem asks whether the cauchy dual operator t t t t 1 of a 2 isometry t is subnormal in the present paper we show that the problem has a negative solution the first counterexample depends heavily on a reconstruction theorem stating that if t is a 2 isometric weighted shift on a rooted directed tree with nonzero weights that satisfies the perturbed kernel condition then t is subnormal if and only if t satisfies the unperturbed kernel condition the second counterexample arises from a 2 isometric adjacency operator of a locally finite rooted directed tree again by thorough investigations of positive solutions of the cauchy dual subnormality problem in this context we prove that if t is a 2 isometry satisfying the kernel condition or a quasi brownian isometry then t is subnormal we construct a 2 isometric adjacency operator t of a rooted directed tree such that t does not satisfy the kernel condition t is not a quasi brownian isometry and t is subnormal

some results on the convex combination of uninorms abstract it is well known that under some conditions a convex combination of the drastic product t d and the strict triangular norm is still a triangular norm uninorms as a special kind of generalization of both triangular norms and triangular conorms have been widely used in fuzzy set theory in this paper the convex combination of uninorms is studied some properties of the class of uninorms with the underlying triangular norm t d are presented firstly then the convex combination of this class of uninorms is discussed and it is shown that only in some trivial cases the convex combination is still a uninorm

asymptotic behaviour and cyclic properties of weighted shifts on directed trees abstract in this paper we investigate a new class of bounded operators called weighted shifts on directed trees introduced recently in 11 this class is a natural generalization of the so called weighted bilateral unilateral and backward shift operators in the first part of the paper we calculate the asymptotic limit and the isometric asymptote of a contractive weighted shift on a directed tree and that of the adjoint then we use the asymptotic behaviour and similarity properties in order to obtain cyclicity results we also show that a weighted backward shift operator is cyclic if and only if there is at most one zero weight

on distributivity equations for uninorms over semi t operators recently dryga generalized nullnorms and t operators and introduced semi t operators by eliminating commutativity from the axioms of t operators distributivity equations were investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we give out the solutions of distributivity equations for uninorms over semi t operators previous results about distributivity equations for uninorms over nullnorms can be obtained as corollaries

the modularity condition for uninorms revisited abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory the modularity equation is a kind of restricted general associative equations in the literature the already known results concerning the modularity equation for two uninorms are based on the assumption that both uninorms lie in one of the most studied classes of uninorms in this study we explore the modularity equation involving uninorms in a most general setting specifically we investigate the modularity between two uninorms in the cases when one uninorm belongs to any of the most studied classes of uninorms but the other one is any uninorm with no further assumptions further many new solutions appear from this new point of view that were not included in previous approaches

a characterization of a class of uninorms with continuous underlying operators in this paper all uninorms locally internal in the region a e given by the complement in 0 1 2 of 0 e 2 e 1 2 where e is the neutral element of the uninorm having continuous underlying operators are studied and characterized by distinguishing some cases when the underlying t norm and t conorm are not given by ordinal sums it is proved that uninorms locally internal in a e are in fact all possible uninorms with these underlying operators except when both the t norm and the t conorm are strict in which case there is also the class of representable uninorms leading to a finite number of possibilities when at least one of the continuous underlying operators is given by an ordinal sum again there are other possible uninorms than those that are locally internal in a e but all uninorms with this property are also characterized in this case infinitely many possibilities can appear depending on the set of idempotent elements of the uninorm

van melle s combining function in mycin is a representable uninorm an alternative proof abstract recently tsadiras and margaritis have shown that the function implemented in the expert system mycin for combining certainty factors is a uninorm in this paper we present a compact alternative to the given direct and lengthy proof based on the construction of representable uninorms by means of an additive generator consequently we show that van melle s combining function is a representable uninorm in fact it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum

conditional distributivity equation for uninorms with continuous underlying operators our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory and focused also by klement in the linz seminar 2000 closing session this paper is mainly devoted to solving the functional equations of conditional distributivity of u 1 over u 2 where both u 1 and u 2 are uninorms with continuous underlying operators then the almost complete characterization of such a pair u 1 u 2 of uninorms is given except for only a small fraction of the unit square next we give the complete characterization of the previous pair under some appropriate restriction that is the second operator u 2 in mathbf u max cup mathbf u min finally we also construct a counterexample to illustrate that the obtained results are necessary but not sufficient for general cases with unlimited condition

uninorms continuous on 0 e 2 e 1 2 uninorms continuous on 0 e 2 e 1 2 are discussed archimedean uninorms continuous and cancellative on 0 e 2 e 1 2 are characterized and related non archimedean uninorms are also discussed the problem when is the border continuous projection of a t norm associative i e a t subnorm is also answered

the group of fractions of a torsion free lcm monoid is torsion free abstract we improve and shorten the argument given in j algebra 210 1998 291 297 in particular the fact that artin braid groups are torsion free now follows from garside s results almost immediately

gaussian groups are torsion free abstract assume thatgis a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain thengis torsion free the result applies in particular to all finite coxeter type artin groups

characterizing set valued functions of uninorms with continuous underlying t norm and t conorm abstract the uninorms with continuous underlying functions were characterized by their set of discontinuity points in the previous work of the author using the characterizing set valued function in this paper properties of this characterizing set valued function are studied it is shown that the type of the monotonicity of such a set valued function is always changed in idempotent points of the corresponding uninorm several additional properties of the characterizing set valued function of a uninorm with continuous underlying functions are shown and an example is included results shown in this paper are used for a complete characterization of uninorms with continuous underlying functions via the ordinal sum construction which is shown in the consecutive paper

the distributivity equation for uninorms revisited abstract the distributivity equation has been widely studied involving different classes of aggregation functions from t norms and t conorms to uninorms nullnorms and generalizations of them it is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing since uninorms have been used in these topics the study of the distributivity between two uninorms becomes specially interesting in a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone in this paper we want to achieve this study by focusing on the reverse direction that is for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm we show along the paper that this new point of view leads to many new solutions

a garside theoretic approach to the reducibility problem in braid groups abstract let d n denote the n punctured disk in the complex plane where the punctures are on the real axis an n braid is said to be reducible if there exists an essential curve system c in d n called a reduction system of such that c c where c denotes the action of the braid on the curve system c a curve system c in d n is said to be standard if each of its components is isotopic to a round circle centered at the real axis in this paper we study the characteristics of the braids sending a curve system to a standard curve system and then the characteristics of the conjugacy classes of reducible braids for an essential curve system c in d n we define the standardizer of c as st c p b n p c is standard and show that st c is a sublattice of b n in particular there exists a unique minimal element in st c exploiting the minimal elements of standardizers together with canonical reduction systems of reducible braids we define the outermost component of reducible braids and then show that for the reducible braids whose outermost component is simpler than the whole braid including split braids each element of its ultra summit set has a standard reduction system this implies that for such braids finding a reduction system is as easy as finding a single element of the ultra summit set

garside groups are strongly translation discrete abstract in this paper we show that all garside groups are strongly translation discrete that is the translation numbers of non torsion elements are strictly positive and for any real number r there are only finitely many conjugacy classes of elements whose translation numbers are less than or equal to r it is a consequence of the inequality inf s g inf s g n n inf s g 1 for a positive integer n and an element g of a garside group g where inf s denotes the maximal infimum for the conjugacy class we prove the inequality by studying the semidirect product g n z g n of the infinite cyclic group z and the cartesian product g n of a garside group g which turns out to be a garside group we also show that the root problem in a garside group g can be reduced to a conjugacy problem in g n hence the root problem is solvable for garside groups

on properties of uninorms locally internal on the boundary abstract recently a class of uninorms locally internal on the boundary was proposed by mas et al during the study of the migrativity property for uninorms in this paper some properties of this class of uninorms are presented and the characterizations are obtained for different cases

an extension of the migrative property for uninorms in this paper the notion of a migrative uninorms over a fixed uninorm u 0 with the same neutral element is introduced all uninorms u that are a migrative over a uninorm u 0 are studied all cases when u and u 0 have continuous underlying operations and belong to any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for all possible combinations

an isoperimetric inequality for artin groups of finite type we show that artin groups of finite type satisfy a quadratic isoperimetric inequality moreover we describe an explicit algorithm to solve the word problem in quadratic time

properties of uninorms with the underlying operations given as ordinal sums abstract uninorms as mixed aggregation operations on the unit interval have been widely used as logical connectives in fuzzy set theory this paper presents some properties of uninorms for which the underlying operations are given as ordinal sums specially we present the relations between two arbitrary summands and the value on cartesian product of their underlying intervals one in 0 e and the other in e 1 where e is neutral element of the uninorm whose results bring us a step closer to the structure of uninorms that have continuous underlying operations as a byproduct we characterize several special classes of uninorms that are different from the well studied classes of uninorms

distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t conorm this paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms in particular the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict from the obtained results it is deduced that distributivity and conditional distributivity are equivalent moreover we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict

a shimorin type analytic model on an annulus for left invertible operators and applications abstract a new analytic model for left invertible operators which extends both shimorin s analytic model for left invertible and analytic operators and gellar s model for bilateral weighted shift is introduced and investigated we show that a left invertible operator t which satisfies certain conditions can be modeled as a multiplication operator m z on a reproducing kernel hilbert space of vector valued analytic functions on an annulus or a disc a similar result for composition operators in l 2 spaces is established

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

migrativity property for uninorms and semi t operators in this paper the notions of migrative uninorms over semi t operators and migrative semi t operators over uninorms are introduced and investigated all solutions of the migrativity equations for all possible combinations of semi t operators and uninorms are characterized

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

characterization of uninorms with continuous underlying t norm and t conorm by their set of discontinuity points uninorms with continuous underlying t norm and t conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown this set is proved to be a subset of the graph of a special symmetric u surjective nonincreasing set valued function which gives us a necessary condition for a uninorm to have continuous underlying functions a sufficient condition for a uninorm to have continuous underlying operations is also given several examples are included

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

on the distributivity property for uninorms abstract distributivity between two operations is a property that was already posed many years ago and that is especially interesting in the framework of logical connectives for this reason the distributivity property has been extensively studied for several families of operations like triangular norms and conorms some kinds of uninorms and nullnorms also called t operators and even for some generalizations of them in this paper we investigate the distributivity equation involving two uninorms lying in any one of the most studied classes of uninorms leading to many new solutions

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

a note on an extension of the migrative property for uninorms this paper shows by an example that proposition 15 iv c in mas et al 2013 about migrative property for uninorms in u c o s m i n is false and corrects these propositions

compression of quasianalytic spectral sets of cyclic contractions the class l0 h of cyclic quasianalytic contractions was studied in kerchy 2011 12 the subclass l1 h consists of those operators t in l0 h whose quasianalytic spectral set t covers the unit circle t the contractions in l1 h have rich invariant subspace lattices in this paper it is shown that for every operator t l0 h there exists an operator t1 l1 h commuting with t thus the hyperinvariant subspace problems for the two classes are equivalent the operator t1 is found as an h function of t the existence of an appropriate function compressing t to the whole circle is proved using potential theoretic tools by constructing a suitable regular compact set on t with absolutely continuous equilibrium measure

braid groups and left distributive operations the decidability of the word problem for the free left distributive law is proved by introducing a structure group which describes the underlying identities this group is closely connected with artin s braid group b braid colourings associated with free left distributive structures are used to show the existence of a unique ordering on the braids which is compatible with left translation and such that every generator ai is preponderant over all ak with k i this ordering is a linear ordering the first goal of the present paper is to give a proof of the following result which had been conjectured for several years theorem there is an effective algorithm for deciding whether a given identity is or is not a consequence of the left distributivity identity x yz xy xz until recently this question has had a rather unusual status conditional solutions were given independently in 6 and 24 where the decision problem was reduced to a specific algebraic hypothesis one which had been shown by richard laver to be a consequence of a very strong set theoretical axiom of a type which certainly cannot be derived from the usual axioms of set theory namely a large cardinal axiom the question as to whether a strong axiom of this type was actually needed remained open opinions were in fact divided a connection between large cardinals and a purely finitistic problem of this caliber would seem paradoxical but it is well known that problems of a combinatorial type can embody surprisingly strong proof principles see for instance 28 and some work on free distributive structures has shown that they do give rise to intrinsically complex objects typically nonprimitive recursive ones cf 12 13 we will show that in the present case a solution which is purely algebraic in terms of the methods employed and the spirit of the argument can in fact be given in particular no unusual set theoretical axioms are required for this argument the decision method described in 6 was fully effective but the proof of the correctness of the algorithm amounted to a direct invocation of this specific algebraic hypothesis which followed from a large cardinal axiom with no hint of a direct proof we shall refine this decision method below introducing uniqueness at each step of the process and the correctness will then be seen to follow very naturally received by the editors february 5 1993 1991 mathematics subject classification primary 20f36 1 7a30 1 7a50

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05

ordering based on uninorms in this paper an order induced by uninorms on bounded lattices is given and discussed by defining such an order the t partial order is extended to a more general form the relationship between the order induced by the underlying t norm and t conorm and the order induced by a uninorm is studied finally the order is extended to the order induced by n uninorms on chains

a single point characterization of representable uninorms we study uninorms of which both the underlying t norm and underlying t conorm are strict such uninorms are the only candidates for being representable by an additive generator we prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the remaining open part of the unit square more explicitly such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments if this single value coincides with one of these bounds then the value of the uninorm at any point in the remaining open part is determined by the same bound

an equivalence relation based on the u partial order abstract in this paper an equivalence relation on the class of uninorms induced by the u partial order is discussed defining the set of all incomparable elements w r t the u partial order this set is deeply investigated and some relations with the sets of all incomparable elements w r t the orders induced by the corresponding underlying t norm and t conorm are presented also the set of all incomparable elements with a fixed element w r t the u partial order is defined and studied in detail

remarks on uninorm aggregation operators it is proved that continuous uninorm aggregation operators are only t norms or t conorms some general constructions about uninorm aggregation operators are given

complete positive group presentations abstract a combinatorial property of positive group presentations called completeness is introduced with an effective criterion for recognizing complete presentations and an iterative method for completing an incomplete presentation we show how to directly read several properties of the associated monoid and group from a complete presentation cancellativity or existence of common multiples in the case of the monoid or isoperimetric inequality in the case of the group in particular we obtain a new criterion for recognizing that a monoid embeds in a group of fractions typical presentations eligible for the current approach are the standard presentations of the artin tits groups and the heisenberg group