arrow categories goguen categories were introduced as a suitable categorical description of l fuzzy relations i e of relations taking values from an arbitrary complete brouwerian lattice l instead of the unit interval 0 1 of the real numbers in this paper we want to study the algebraic structures derived from goguen categories by replacing its second order axiom by some weaker versions

an algebraic formalization of fuzzy relations abstract this paper provides an algebraic formalization of mathematical structures formed by fuzzy relations with sup min composition a simple proof of a representation theorem for boolean relation algebras satisfying tarski rule and point axiom has been given by schmidt and strohlein unlike boolean relation algebras fuzzy relation algebras are not boolean but equipped with semi scalar multiplication first we present a set of axioms for fuzzy relation algebras and improve the definition of point relations then by using relational calculus a representation theorem for such relation algebras is deduced without tarski rule

riemann stieltjes operators and multipliers on q p spaces in the unit ball of c n this paper is devoted to characterizing the riemann stieltjes operators and pointwise multipliers acting on mobius invariant spaces q p which unify bmoa and bloch space in the scale of p the boundedness and compactness of these operators on q p spaces are determined by means of an embedding theorem i e q p spaces boundedly embedded in the non isotropic tent type spaces t q infinity c 2010 elsevier inc all rights reserved

composition operators from f p q s spaces to the nth weighted type spaces on the unit disc abstract in this note we characterize the boundedness and compactness of the composition operator from the general function space f p q s to the nth weighted type space on the unit disk where the nth weighted type space has been recently introduced by stevo stevic

composition operators on qk spaces abstract suppose that is a nonconstant analytic self map of the unit disk d compactness of composition operator c between two mobius spaces q k 1 and q k 2 is studied moreover necessary and sufficient condition for c from the dirichlet space d to a general class of analytic functions f p q s to be compact is given in terms of the map

squares and rectangles in relation categories three cases semilattice distributive lattice and boolean non unitary in this paper we investigate rectangle morphisms of dedekind categories or semilattice relation categories or unitary allegories which appear to be a basic structure for relation categories in order to reconstruct the dedekind category generated by all the rectangle morphisms we are obliged to clarify the role of both the square morphisms and the functions s which assign to every square morphism c the ideal morphism cs 1c1 we translate this observations into adapted new objects that we call the mp families in this way the reconstruction problem becomes an adjunction problem to each dedekind category we associate a mp family to each functor between two dedekind categories we associate a morphism between two mp families this association is a functor this functor has a left adjoint this result is also true for other universes distributive lattices boolean algebras

on an integral type operator from logarithmic bloch type and mixed norm spaces to bloch type spaces abstract this paper studies the boundedness and compactness of the following integral type operator recently introduced by this author p g f z 0 1 f t z g t z d t t z b where is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type and mixed norm spaces to bloch type spaces

on an integral type operator from ω bloch spaces to µ zygmund spaces let h b denote the space of all holomorphic functions on the unit ball b c n we study the boundedness and compactness of the following integral type operatorp g f z 0 1f tz g tz dtt f h b z b where g h b and g 0 0 from w bloch spaces to m zygmund spaces

on a product type operator from bloch spaces to weighted type spaces on the unit ball we characterize the boundedness and compactness of a product of radial derivative composition and multiplication operators from bloch spaces to weighted type spaces on the unit ball

composition operators from the space of cauchy transforms to bloch and the little bloch type spaces on the unit disk abstract we completely characterize the boundedness and compactness of composition operators from the space of cauchy transforms on the unit disk d into the bloch type space b as well as the little bloch type space b 0 consisting respectively of all holomorphic functions f on d such that sup z d z f z that is of all holomorphic functions f on d such that lim z 1 z f z 0 for some weight function as a byproduct of our results norm of the operator is calculated when b is replaced by b c

categories of relations for variable basis fuzziness arrow categories establish a categorical and algebraic description of l fuzzy relations i e relations that use membership values from an arbitrary but fixed complete heyting algebra l with other words arrow categories describe the fixed basis case in this paper we are interested in the variable basis case i e the case where relations between different objects may use different membership values we will investigate the structure of the collection of lattices of membership values within a given dedekind category this will lead to a complete characterization of the variable basis case in this context

shape sensitivity in elasto plastic computations an algorithm for design sensitivity analysis of elasto plastic response for the case of design dependent geometry is discussed the domain parametrization approach is employed some important implications for the concept of isoparametric element formulation are indicated the idea of shape sensitivity computations is similar to that of sensitivity with respect to material parameters however derivation of additional geometric matrices and integral expressions is necessary a possible discontinuity of sensitivity solutions is indicated and it is shown that the algorithm handles it correctly a plane stress computational example illustrates the application of the method

isometric composition operators on the analytic besov spaces abstract we investigate the isometric composition operators on the analytic besov spaces for 1 p 2 we show that an isometric composition operator is induced only by a rotation of the disk for p 2 we extend previous work on the subject finally we analyze this same problem for the besov spaces with an equivalent norm

composition operators from bloch type spaces into qk type spaces supposeis an analytic map of the unit disk d into itself x is a banach space of analytic functions on d define the composition operator c cf f for all f x in this paper the boundedness and compactness of the composition operators from bloch spaces into qk p q and qk 0 p q spaces are discussed where 0 keywords composition operator analytic function bspace k carleson measure compact k carleson measure

weighted composition operators from the besov spaces into the weighted type space hμ abstract let denote a positive continuous function on the open unit disk d in this work we characterize the bounded weighted composition operators from the analytic besov spaces b p 1 p into the weighted type space h consisting of the analytic functions on d such that sup z d z f z and determine their operator norms we also determine the essential norm of the bounded weighted composition operators acting on the dirichlet space and obtain explicit estimates when p 1 in the general case when the operator maps b p into h we derive an approximation of the essential norm that yields a characterization of the compact weighted composition operators finally we derive characterizations of the bounded and the compact weighted composition operators from the spaces of antiderivatives of functions in b p and b m o a into the bloch spaces

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

integral type operators from iterated logarithmic bloch spaces to zygmund type spaces let h b denote the space of all holomorphic functions on the unit ball b of c n and rh z j 1 nz j h z j z the radial derivative of h in this paper we study the boundedness and compactness of the following integral operator t g f z 0 1f tz rg tz dtt f h b z b from iterated logarithmic bloch spaces to zygmund type spaces

products of composition and differentiation operators from zygmund spaces to bloch spaces and bers spaces abstract the boundedness and compactness of the products of differentiation and composition operators from zygmund spaces to bloch spaces and bers spaces are discussed in this paper

membership values in arrow categories in this paper we consider an internal representation of the lattice of membership values used by the relations in an arbitrary arrow category this is achieved by defining a more general construction that pairs regular with membership values in one object we will show basic properties of this construction including its relationship to the lattice of membership values this characterization of the lattice of membership values allows to specify and reason about the lattice elements as elements of an object of the category furthermore this representation also leads to an abstract approach to higher order fuzziness based on arrow categories

composition operators on zygmund spaces of the unit ball abstract in this paper we give some new characterizations of the zygmund space and the little zygmund space of the unit ball in c n we further characterize the boundedness and compactness of composition operators on these spaces

weighted composition operators from area nevanlinna spaces into bloch spaces let h d denote the class of all analytic functions on the open unit disk d of c let f be an analytic self map of d and u h d the weighted composition operator is defined by uc ff z u z f f z f h d the boundedness and compactness of weighted composition operators from area nevanlinna spaces into bloch spaces and little bloch spaces are characterized in this paper

design sensitivity analysis in large deformation elasto plastic and elasto viscoplastic problems implicit time integration algorithm derived by simo for his large deformation elasto plastic constitutive model is generalized for the case of isotropy and associative flow rule towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters combining it with the general formulation of design sensitivity analysis dsa for non linear finite element transient equilibrium problem we come at a numerically efficient closed form finite element formulation of dsa for large deformation elasto plastic and elasto viscoplastic problems with various types of design variables material constants shape parameters the paper handles several specific issues like the use of a non algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change computational examples demonstrate abilities of the formulation and quality of results copyright 2005 john wiley sons ltd

integral type operators from bloch type spaces to zygmund type spaces let h b denote the space of all holomorphic functions on the unit ball email protected c n this paper investigates the following integral type operator with symbol email protected h b t g f z email protected 0 1f tz rg tz dtt email protected h b email protected b where rg z email protected j 1 nz email protected email protected z j z is the radial derivative of g the boundedness and compactness of the operator t g from bloch type spaces to zygmund type spaces are studied

weighted differentiation composition operators from h and bloch spaces to nth weighted type spaces on the unit disk we characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions the bloch space and the little bloch space to nth weighted type spaces on the unit disk

weighted composition operators from weighted bergman spaces to weighted type spaces on the unit ball we calculate the operator norm of the weighted composition operator from a weighted bergman space to a weighted type space on the unit ball of c n we also characterize the compactness of the operator

on an integral type operator from iterated logarithmic bloch spaces into bloch type spaces let h b denote the space of all holomorphic functions on the open unit ball b of c n let f f 1 f n be a holomorphic self map of b and email protected h b such that g 0 0 in this paper we study the boundedness and compactness of the following integral type operator recently introduced by xiangling zhu and the second authori f gf z email protected 0 1rf f tz g tz dtt email protected b from the iterated logarithmic bloch spaces into the bloch type spaces for the case when f z z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic bloch space into the little bloch type space

operator norms and essential norms of weighted composition operators between banach spaces of analytic functions abstract in this work we characterize the bounded and compact weighted composition operators from a large class of banach space of analytic functions on the open unit disk into weighted banach spaces determine the operator norm exactly and obtain estimates on the essential norm we obtain an exact formula of the essential norm when such operators map the hardy spaces the weighted bergman spaces the bloch space and the little bloch space into the banach space h where the weight is a continuous function in this general setting we also study such operators when the target space is an bloch space for any 0 and more generally any bloch type space as special cases we derive norm and essential norm approximations for the operators acting on the hardy spaces and the weighted bergman spaces immediate corollaries are results on certain integral operators

the material time derivative of logarithmic strain abstract in this article we derive explicit formulas for the time rate of change of the logarithmic strains ln u and ln v where u and v are the right and left stretch tensors respectively results are obtained in both two and three dimensions for the cases where the principal stretches are repeated as well as for the case where they are distinct the formulas are displayed in terms of v the stretching tensor d the rotation r and the principal stretches finally we consider the corotational and jaumann derivatives of ln v and establish conditions under which these logarithmic strain rates are equal to the stretching tensor

geometric models and compactness of composition operators abstract this work explores some of the terrain between functional equations geometric function theory and operator theory it is inspired by the fact that whenever a composition operator or one of its powers is compact on the hardy space h 2 then its eigenfunctions cannot grow too quickly on the unit disc the goal is to show that under certain natural and necessary additional conditions there is a converse slow growth of eigenfunctions implies compactness we interpret the slow growth condition in terms of the geometry of the principal eigenfunction of the composition operator the konigs function of the inducing map we emphasize throughout the importance of this eigenfunction in providing a simple geometric model for the operator s inducing map

compact composition operators on besov spaces we give a carleson measure characterization of the compact composition operators on besov spaces we use this characterization to show that every compact composition operator on a besov space is compact on the bloch space finally we give conditions that guarantee that the converse holds

composition type operator from bergman space to μ bloch type space in cn abstract let be a holomorphic self map of b and h b a composition type operator t is defined by t f f we can regard this operator as a generalization of a multiplication operator and a composition operator for normal functions some necessary and sufficient conditions are given for which t is a bounded or compact operator from bergman space to bloch type space on the unit ball of c n as a corollary we obtain the pointwise multiplier from bergman space to bloch type space on b

differences of generalized composition operators on the bloch space abstract the boundedness and compactness of the differences of two generalized composition operators on the bloch space in the unit disk are investigated in this paper

on new bloch type spaces we introduce a new bloch type space so called the logarithmic bloch type space b l o g b a d on the unit disc d as the space of all holomorphic functions f on d such thatsupz d 1 z alne b a1 z b f z 0 and b 0 and present some basic properties of the space a necessary and a sufficient condition for a function with hadamard gaps to belong to the logarithmic bloch type space are given as well as some applications of these results to a composition operator

calculation of eigenvector derivatives for structures with repeated eigenvalues in structural optimization and system identification eigenvector derivatives provide important information for updating design model parameters when the current parameter values yield repeated eigenvalues it has not been possible previously to calculate unique eigenvector derivatives recent work has provided a method for determining unique eigenvalue derivatives for this case but methods for calculating the eigenvector sensitivities have been incomplete in this work a complete method for calculation of repeated root eigenvector derivatives is shown for the real symmetric structural eigenproblem the derivation is completed by using information from the second derivative of the eigen problem and is limited to the case of distinct eigenvalue sensitivities as an example the repeated root eigenvector sensitivities are calculated for a simple three degree of freedom beam grillage comparisons of linear approximations using these derivatives to the calculated eigenvectors support the accuracy of the formulation

carleson sobolev measures for weighted bloch spaces abstract carleson sobolev measures for weighted bloch spaces on the unit ball of c n are described the classical carleson measures for growth spaces on special circular domains are characterized

representation theory of goguen categories goguen categories constitute a suitable algebraic formalisation for l fuzzy relations it is well known that an l fuzzy relation may be represented by the set of all its cuts the aim of this paper is to show a similar result for goguen categories furthermore given an algebraic structure of relations a dedekind category r and a complete brouwerian lattice l the idea above allows us to define a goguen category g such that the underlying structures are r and l using our pseudo representation theorem we show that the representation theory of goguen categories is equivalent to the representation theory of simple dedekind categories this result allows us to transfer known representation results for dedekind categories to the theory of goguen categories

a new algebraic approach to l fuzzy relations convenient to study crispness abstract the aim of this paper is to develop a suitable calculus of l fuzzy relations we show that for this purpose the theory of dedekind categories is too weak therefore we introduce the notion of a goguen category as a suitable algebraic definition and show several properties of this kind of a relational category

dedekind categories with cutoff operators dedekind categories provide a suitable categorical framework for lattice valued binary relations it is known that the notion of crispness cannot be described by the basic tools of this theory only in this paper we will study dedekind categories with a cutoff operator in order to circumvent this shortage we will introduce and investigate the properties of the operator and its relationship with other tools previously used for the same purpose the main result of this paper is a representation theorem for dedekind categories with a cutoff operator satisfying the point axiom

sensitivity analysis for dynamic mechanical systems with finite rotations this paper presents a sensitivity analysis for dynamic systems with large rotations using a semi analytical direct differentiation technique the choice of a suitable time integration strategy for the rotation group appears to be critical for the development of an efficient sensitivity analysis three versions of the generalized time integration scheme are considered a residual form a linear form and a geometric form their consistency is discussed and we show that the residual form which is the most direct extension of the generalized algorithm defined in structural dynamics should not be used for problems with large rotations the sensitivity analysis is performed and close connections are highlighted between the structure of the sensitivity equations and of the linearized dynamic equations hence algorithms developed for the original problem can be directly reused for the sensitivities finally a numerical example is analysed in detail copyright 2007 john wiley sons ltd

level sets and composition operators on the dirichlet space abstract we consider composition operators in the dirichlet space of the unit disc in the plane various criteria on boundedness compactness and hilbert schmidt class membership are established some of these criteria are shown to be optimal

weighted composition operators from zygmund spaces into bloch spaces abstract let be an analytic self map and u be a fixed analytic function on the open unit disk d in the complex plane c the weighted composition operator is defined by uc f z u z f z z d f h d this paper studies the boundedness and compactness of weighted composition operators from zygmund spaces into bloch spaces

on some integral type operators between a general space and bloch type spaces abstract the boundedness and compactness of the next integral operators p g f z 0 1 f tz g tz dt t and l g f z 0 1 r f tz g tz dt t between f p q s spaces and bloch type spaces on the unit ball of c n are studied among other results we solve some open problems and considerably extend results in the paper li and stevic compactness of riemann stieltjes operators between f p q s and bloch spaces publ math debrecen 72 1 2 2008 111 128

bloch functions on bounded symmetric domains we introduce and characterize bloch functions on bounded symmetric domains which may be infinite dimensional by extending several well known equivalent conditions for bloch functions on the open unit disc u in cc we also generalize a number of results concerning bloch functions on u to bounded symmetric domains given a holomorphic mapping between bounded symmetric domains bxbx and byby we derive criteria for boundedness and compactness of the composition operator c c between the bloch spaces b by b by and b bx b bx extending several known results for finite dimensional domains

compact composition operators on the bloch space of the unit ball abstract in this paper we give several new necessary and sufficient conditions for the compactness of the composition operator c on the bloch space of the unit ball b n

a class of integral operators on spaces of analytic functions abstract we determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators t f z z 1 1 z 0 z f 1 1 d acting on either the analytic besov spaces or other banach spaces of analytic functions on the unit disc including the classical hardy and weighted bergman spaces as well as certain dirichlet spaces and generalized bloch spaces our results unify and extend recent work by aleman and persson 2 the current authors 4 and albrecht and miller 1

composition operators from logarithmic bloch spaces to weighted bloch spaces we characterize the analytic self maps f of the unit disk d in c that induce continuous composition operators c f from the log bloch space b l o g d to m bloch spaces b m d in terms of the sequence of quotients of the m bloch semi norm of the nth power of f and the log bloch semi norm of the nth power f n of the identity function on d where m d 0 is continuous and bounded we also obtain an expression that is equivalent to the essential norm of c f between these spaces thus characterizing f such that c f is compact after finding a pairwise norm equivalent family of log bloch type spaces that are defined on the unit ball b n of c n and include the log bloch space we obtain an extension of our boundedness compactness essential norm results for c f acting on b l o g to the case when c f acts on these more general log bloch type spaces

norm essential norm and weak compactness of weighted composition operators between dual banach spaces of analytic functions abstract in this paper we estimate the norm and the essential norm of weighted composition operators from a large class of non necessarily reflexive banach spaces of analytic functions on the open unit disk into weighted type banach spaces of analytic functions and bloch type spaces we also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of banach spaces of analytic functions that includes a large family of conformally invariant spaces like bmoa and analytic besov spaces

reverse estimates in growth spaces let h b d denote the space of holomorphic functions on the unit ball b d of mathbb c d given a radial doubling weight w we construct functions f g in h b 1 such that f g is comparable to w also we obtain similar results for b d d 2 and for circular strictly convex domains with smooth boundary as an application we study weighted composition operators and related integral operators on growth spaces of holomorphic functions

carleson measures for besov spaces on the ball with applications abstract carleson and vanishing carleson measures for besov spaces on the unit ball of c n are characterized in terms of berezin transforms and bergman metric balls the measures are defined via natural imbeddings of besov spaces into lebesgue classes by certain combinations of radial derivatives membership in schatten classes of the imbeddings is considered too some carleson measures are not finite but the results extend and provide new insight to those known for weighted bergman spaces special cases pertain to arveson and dirichlet spaces and a unified view with the usual hardy space carleson measures is presented by letting the order of the radial derivatives tend to 0 weak convergence in besov spaces is also characterized and weakly 0 convergent families are exhibited applications are given to separated sequences operators of forelli rudin type gap series characterizations of weighted bloch lipschitz and growth spaces inequalities of fejer riesz and hardy littlewood type and integration operators of cesaro type

on the computation of design derivatives for huber mises plasticity with non linear hardening this paper concerns design sensitivity analysis dsa for an elasto plastic material with material parameters depending on or serving as design variables the considered constitutive model is huber mises deviatoric plasticity with non linear isotropic kinematic hardening one which is applicable to metals the standard radial return algorithm for linear hardening is generalized to account for non linear hardening functions two generalizations are presented in both the non linearity is treated iteratively but the iteration loop contains either a scalar equation or a group of tensorial equations it is proven that the second formulation which is the one used in some parallel codes can be equivalently brought to a scalar form more suitable for design differentiation the design derivatives of both the algorithms are given explicitly enabling thus calculation of the explicit design derivative of stresses entering the global sensitivity equation the paper addresses several issues related to the implementation and testing of the dsa module among them the concept of verification tests both outside and inside a fe code as well as the data handling implied by the algorithm the numerical tests which are used for verification of the dsa module are described they shed light on a the accuracy of the design derivatives by comparison with finite difference computations and b the effect of the finite element formulation on the design derivatives for an isochoric plastic flow copyright 2003 john wiley sons ltd

weighted composition operators between large fock spaces in several complex variables abstract let be an entire self map of c n and let u be an entire function on c n a weighted composition operator induced by with weight u is given by u c f z u z f z for z in c n and f is an entire function on c n in this paper we study weighted composition operators acting between two large weighted fock spaces f p and f q we characterize the bounded compact and schatten class membership operators u c acting from f p to f q when 0 p and 0 q our results use certain integral transforms that generalize the usual berezin transform

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

products of composition multiplication and radial derivative operators from logarithmic bloch spaces to weighted type spaces on the unit ball abstract let h b denote the space of all holomorphic functions on the unit ball b of c n h b and be a holomorphic self map of b let c m and r denote the composition multiplication and radial derivative operators respectively in this paper we characterize the boundedness and compactness of linear operators induced by products of these operators from logarithmic bloch spaces to weighted type spaces on the unit ball

ergodic properties of composition operators on banach spaces of analytic functions abstract the composition operators defined on little bloch spaces bergman spaces hardy spaces or little weighted bergman spaces of infinite type when well defined are shown to be mean ergodic if and only if they are power bounded if and only if the symbol has an interior fixed point for these operators uniform mean ergodicity is equivalent to quasicompactness in the sense of yosida and kakutani