associativity of triangular norms characterized by the geometry of their level sets associativity of triangular norms is an algebraic property which unlike for example their commutativity is usually understood as hardly visually interpretable this problem has been studied intensively in the last decade and as a result geometric symmetries of triangular norms with involutive level sets have been revealed the presented paper intends to introduce a different approach which gives more general results the inspiration is taken from web geometry a branch of differential geometry and its concept of reidemeister closure condition which is known to provide a geometric characterization of associativity of loops the paper shows that this concept can be adopted successfully for triangular norms so that it characterizes their associativity in a similar way moreover the offered adaptation preserves the beneficial transparency and simplicity of the reidemeister closure condition this way a visual characterization of the associativity based on the geometry of the level sets is provided for general continuous and continuous archimedean triangular norms

conic aggregation functions inspired by the notion of conic t norms we introduce conic aggregation functions such aggregation functions are completely characterized by their zero set special classes of binary conic aggregation functions such as conic quasi copulas and conic copulas are considered we provide the necessary and sufficient conditions on the boundary curve of the zero set of a conic aggregation function to obtain a conic quasi copula and conclude that the class of conic copulas is a proper subclass of the class of conic quasi copulas moreover we characterize the class of singular conic copulas we investigate some aggregations of conic quasi copulas some examples are also provided

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

continuity of left continuous triangular norms with special associated negations abstract first we show that the class of left continuous triangular norms whose associated negations are discontinuous only at one point is not generally continuous except for the trivial case second we find the strongest left continuous triangular norm with a given associated negation and shows that there is no weakest left continuous triangular norm with a given associated negation

hyperplane complements of large type let f2 be an open convex subset of a finite dimensional real vectorspace v and m a collection of linear hyperplanes we shall suppose that m is locally finite on f2 this means that each point of f2 has a neighborhood meeting only finitely many hyperplanes in m as in 2 chap 5 f2 is partitioned by m in facets recalling that a plinth is a codimension 2 facet we shall say that m is of large type on f2 if for each plinth p its multiplicity m m p c m 3 the main result of the paper is the following

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

proof of the k pi 1 conjecture for affine artin groups we prove the k pi 1 conjecture for affine artin groups the complexified complement of an affine reflection arrangement is a classifying space this is a long standing problem due to arnol d pham and thom our proof is based on recent advancements in the theory of dual coxeter and artin groups as well as on several new results and constructions in particular we show that all affine noncrossing partition posets are el shellable we use these posets to construct finite classifying spaces for dual affine artin groups we introduce new cw models for the orbit configuration spaces associated with arbitrary coxeter groups we construct finite classifying spaces for the braided crystallographic groups introduced by mccammond and sulway

artin groups and infinite coxeter groups if the associated coxeter group 7 is finite for the braid group b the associated coxeter group is the symmetric group s brieskorn and saito 4 and independently deligne 6 have investigated artin groups of finite type in 1969 garside 7 solved the conjugacy problem for braid groups brieskorn this work was supported by nsf grants mcs 7902512 and mcs 7703452 the authors would like to thank the referee for an extremely careful reading of the paper and many helpful sugges tions

surfaces with pg q 3 we classify minimal complex surfaces of general type with p g q 3 more precisely we show that such a surface is either the symmetric product of a curve of genus 3 or a free z 2 quotient of the product of a curve of genus 2 and a curve of genus 3 our main tools are the generic vanishing theorems of green and lazarsfeld and the characterization of theta divisors given by hacon in corollary 3 4 of fourier transforms generic vanishing theorems and polarizations of abelian varieties

rotation invariant t norms where triple rotation and rotation annihilation meet generalizing the notion of a zoom of a t norm not only allows to extend the triple rotation method and its corresponding decomposition but also allows to describe the interface between the triple rotation method and the rotation annihilation method an alternative view on the partition behind the rotation annihilation method is required to make both methods compatible besides zooms we also use contour lines and the companion of a t norm to concisely formulate the results

a construction method of semicopulas from fuzzy negations in this paper a method of defining commutative semicopulas from fuzzy negations is introduced some properties are investigated that lead to understand these semicopulas as non associative generalizations of the lukasiewicz t norm in particular it is proved that some well known examples of copulas and t norms can be obtained by this method moreover any commutative semicopula constructed by this method can be always obtained from a negation n which is symmetric with respect to the diagonal then those symmetric fuzzy negations n for which the corresponding semicopula is a copula are characterized also several examples of symmetric negations n are given such that the corresponding semicopula is a t norm

co rotation annihilations of residuated semigroups two new ways to construct involutive residuated semigroups are introduced in this paper namely connected and disconnected co rotation annihilations co rotation annihilations utilizes two particular kinds of residuated semigroups to construct a third one the method is suitable for constructing a large class of examples of negative rank involutive fl e algebras that is where the unit element of the algebra is smaller than the falsum constant which defines the involution in the algebra

on the classification of irregular surfaces of general type with nonbirational bicanonical map the present paper is devoted to the classification of irregular surfaces of general type with pg 3 and nonbirational bicanonical map our main result is that if s is such a surface and if s is minimal with no pencil of curves of genus 2 then s is the symmetric product of a curve of genus 3 and therefore pg q 3 and k2 6 furthermore we obtain some results towards the classification of minimal surfaces with pg q 3 such surfaces have 6 kz 9 and we show that kz 6 if and only if s is the symmetric product of a curve of genus 3 we also classify the minimal surfaces with pg q 3 with a pencil of curves of genus 2 proving in particular that for those one has kz 8

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

fibred algebraic surfaces and commutators in the symplectic group abstract we describe the minimal number of critical points and the minimal number s of singular fibres for a non isotrivial fibration of a surface s over a curve b of genus 1 exhibiting several examples and in particular constructing a fibration with s 1 and irreducible singular fibre with 4 nodes then we consider the associated factorizations in the mapping class group and in the symplectic group we describe explicitly which products of transvections on homologically independent and disjoint circles are a commutator in the symplectic group s p 2 g z

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

cancellativity properties for t norms and t subnorms on the one hand cancellativity properties are mainly used to express to which extend the partial functions of a t subnorm t are injective on the other hand the zooms of t corresponding to its non trivial archimedean components are t subnorms that largely determine t fixing one out of four basic types of cancellativity cancellativity conditional cancellativity weak cancellativity and weak conditional cancellativity we figure out which less restrictive type of cancellativity expresses that all maximal archimedean zooms of t satisfy the given cancellativity property we lay bare the mutual relationships between all these types of cancellativity and solve an open problem posed by klement et al

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