non universal critical behaviour in mean field theory of inhomogeneous systems abstract we consider the layered magnetic systems with inhomogeneous inter layer couplings and study their critical properties within the framework of mean field theory we consider two kinds of distribution of the couplings i quasi periodic according to the fibonacci sequence and ii smoothly inhomogeneous in which the couplings deviate from the bulk couplings by an amount of al 2 where l measures the distance from a free surface according to analytical and accurate numerical results the critical behaviour of both the problems is non universal and the corresponding critical exponents are coupling dependent

efficient modal analysis of systems with local stiffness uncertainties the characterization of the uncertainty in modal quantities of an uncertain linear structural system is essential to the rapid determination of its response to arbitrary loadings although the size of many computational structural models used is extremely large i e thousands of equations the uncertainty to be analyzed is oftentimes localized to very small regions of the model this paper addresses the development of an efficient computational methodology for the modal analysis of linear structural systems with local stiffness uncertainties the newly developed methodology utilizes an enriched basis that consists of the sub spectrum of a nominal structural system augmented with additional basis vectors generated from a knowledge of the structure of the stiffness uncertainty in addition methods for determining bounds on the approximate modal frequencies and mode shapes are discussed numerical results demonstrate that the algorithm produces highly accurate results with greatly reduced computational effort copyright 2009 john wiley sons ltd

complex fractal dimensions describe the hierarchical structure of diffusion limited aggregate clusters we analyze large diffusion limited aggregates and uncover a ital discrete scaling invariance in their inner structure which can be quantified by the introduction of a set of ital complex fractal dimensions we provide a theoretical framework and prediction of their values based on renormalization group theory and a previous wavelet analysis copyright ital 1996 the american physical society

on degrees of asymmetry of a copula with respect to a track abstract in this paper we provide lower and upper bounds on the degree of asymmetry of a copula with respect to a track a continuous and strictly increasing curve in the unit square generalizing the problem with respect to the main diagonal we also study an average asymmetry in sections for given tracks finally we also give an asymmetry map with respect to the opposite diagonal

nonuniversal behavior for aperiodic interactions within a mean field approximation we study the spin 1 2 ising model on a bethe lattice in the mean field limit with the interaction constants following one of two deterministic aperiodic sequences the fibonacci or period doubling one new algorithms of sequence generation were implemented which were fundamental in obtaining long sequences and therefore precise results we calculate the exact critical temperature for both sequences as well as the critical exponents ensuremath beta ensuremath gamma and ensuremath delta for the fibonacci sequence the exponents are classical while for the period doubling one they depend on the ratio between the two exchange constants the usual relations between critical exponents are satisfied within error bars for the period doubling sequence therefore we show that mean field like procedures may lead to nonclassical critical exponents

anisotropic heisenberg model on hierarchical lattices with aperiodic interactions a renormalization group approach using a real space renormalization group approximation we study the anisotropic quantum heisenberg model on hierarchical lattices with interactions following aperiodic sequences three different sequences are considered with relevant and irrelevant fluctuations according to the luck harris criterion the phase diagram is discussed as a function of the anisotropy parameter delta such that delta 0 and 1 correspond to the isotropic heisenberg and ising models respectively we find three different types of phase diagrams with general characteristics the isotropic heisenberg plane is always an invariant one as expected by symmetry arguments and the critical behavior of the anisotropic heisenberg model is governed by fixed points on the ising model plane our results for the isotropic heisenberg model show that the relevance or irrelevance of aperiodic models when compared to their uniform counterpart is as predicted by the harris luck criterion a low temperature renormalization group procedure was applied to the classical isotropic heisenberg model in two dimensional hierarchical lattices the relevance criterion is obtained again in accordance with the harris luck criterion

relation between non exchangeability and measures of concordance of copulas abstract an investigation is presented of how a comprehensive choice of five most important measures of concordance namely spearman s rho kendall s tau gini s gamma blomqvist s beta and their weaker counterpart spearman s footrule relate to non exchangeability i e asymmetry on copulas besides these results the method proposed also seems to be new and may serve as a raw model for exploration of the relationship between a specific property of a copula and some of its measures of dependence structure or perhaps the relationship between various measures of dependence structure themselves

final solution to the problem of relating a true copula to an imprecise copula abstract in this paper we solve in the negative the problem proposed in this journal montes et al 2015 13 whether an order interval defined by an imprecise copula contains a copula namely if c is a nonempty set of copulas then c inf c c c and c sup c c c are quasi copulas and the pair c c is an imprecise copula according to the definition introduced in the cited paper following the ideas of p boxes we show that there is an imprecise copula a b in this sense such that there is no copula c whatsoever satisfying a c b so it is questionable whether the proposed definition of the imprecise copula is in accordance with the intentions of the initiators our methods may be of independent interest we upgrade the ideas of dibala et al 2016 7 where possibly negative volumes of quasi copulas as defects from being copulas were studied

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

multivariate imprecise sklar type theorems abstract the omnipotent instrument for modeling multivariate dependence of random variables in standard probability theory has become copulas discovered by a sklar in 1959 only recently omladic and stopar prove that in the bivariate case an analogous role is played by exactly the same copulas for random variables coming from finitely additive probability spaces one of the main results of this paper is that this is true also in the general multivariate case the extension to n dimensions requires a better understanding of quasi copulas the lattice closure of copulas with respect to the pointwise order we need to develop a new equivalent definition of this notion that should be useful in other applications as well another tool we introduce and seems to be new even in the standard probability approach is multivariate quasi distributions we also expand the coherence theory for quasi copulas and quasi distributions to the multivariate situation finally our main result is a multivariate sklar type theorem in the imprecise setting

critical behaviour at an edge the critical behaviour of a magnetic system with o n spin symmetry bounded by two d 1 dimensional hyperplanes meeting at an angle alpha is studied within mean field theory and in d 4 epsilon dimensions new exponents emerge for correlation functions and magnetisation and susceptibilities for spins close to the edge they can be expressed in terms of known bulk and surface exponents together with a single new edge exponent which depends however on the angle alpha this exponent is computed to first order in epsilon

transitivity preserving fuzzification schemes for cardinality based similarity measures abstract a family of fuzzification schemes is proposed that can be used to transform cardinality based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe the family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets in particular the fuzzy set intersections are pointwisely generated by frank t norms the fuzzification schemes are applied to a variety of previously studied rational cardinality based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process

best possible bounds on the set of copulas with given degree of non exchangeability abstract we establish best possible bounds on the set of quasi copulas with given degree of non exchangeability these bounds are shown to be best possible bounds as well for the set of copulas with given degree of non exchangeability and consequently also on the set of bivariate distribution functions of continuous random variables with given margins and given degree of non exchangeability non exchangeability of a quasi copula is measured in the sense of nelsen i e proportional to the maximal absolute difference between this quasi copula and its transpose

a hitchhiker s guide to quasi copulas abstract this paper presents a review of the concept of an n quasi copula starting from the characterization of functions that can be derived from operations on random variables we recall several other characterizations and properties that have been proven in the literature highlighting the differences between the bivariate case and the higher dimensional case additionally we recall several applications of n quasi copulas such as their role in the study of bounds on sets of n copulas we also recall various classes of n quasi copulas that have been studied in the literature finally we present some questions that have not yet been answered in the literature

bell type inequalities for quasi copulas we present all bell type inequalities regarding at most four random events of which not more than two are intersected at the same time reformulating these inequalities in the context of fuzzy probability calculus leads to related inequalities on commutative conjunctors we prove that some of these inequalities hold for quasi copulas or copulas additionally for the important parametric family of frank t norms which are also copulas we identify for each of the inequalities the parameter values for which it is fulfilled thereby completing the results of pykacz and d hooghe

the intersection operation in light of joint observables and bell inequalities in operational probability theory operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs in this paper we first explain the need to extend the concept of the intersection operation in the light of the concept of joint observables then we tried to determine the basic features that characterize any possible definition of the intersection operation furthermore we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories these relations are used first to find a suitable suggestion to define the intersection operation second they are used besides the studies made on bell inequalities in fuzzy probability theory to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of bell inequalities in operational probability theory

dynamic analysis using a reduced basis of exact modes and ritz vectors the problem of obtaining an approximate solution for the response of a structure under dynamic forces is addressed the structure is modeled using mass and stiffness matrices and has n degrees of freedom an dimensional approximation is sought in a subspace defined by an arbitrary m orthogonal array a residual vector which is smaller in magnitude the more accurate the approximation is derived the residual contains two terms one is the error involved representing the force vector in the subspace the other is smaller the better the array leads to m approximate solutions of the exact eigenproblem numerical experiments are performed using arrays that are combinations of exact eigenvectors and of ritz vectors in one case when 11 different 10 dimensional bases are used to approximate the solution of a 60 degree of freedom problem it is found that a root mean square measure of relative error is smallest for the basis formed using the 6 lowest exact eigenvectors plus 4 ritz vectors generated from the spatial distribution of the loading

additive decomposition of fuzzy pre orders fuzzy pre orders reflexive and min transitive fuzzy relations constitute an important class of fuzzy relations by means of an indifference generator a fuzzy pre order can be decomposed additively into two parts an indifference relation and a strict preference relation when using a frank t norm as indifference generator we fully characterize the transitivity of these parts only in case the minimum operator is used as generator both parts are min transitive the transitivity of the indifference relation is determined by the frank t norms while the transitivity of the strict preference relation is determined by transforms of the nilpotent minimum t norm

a full scale sklar s theorem in the imprecise setting abstract in this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal montes et al 2015 13 the main tools we develop in order to do so are 1 a theory on quasi distributions based on an idea presented in a paper by r nelsen with collaborators 2 starting from what is called bivariate p box in the above mentioned paper we propose some new techniques based on what we call restricted bivariate p box and 3 a substantial extension of a theory on coherent imprecise copulas developed by m omladic and n stopar in a previous paper in order to handle coherence of restricted bivariate p boxes a side result of ours of possibly even greater importance is the following every bivariate distribution whether obtained on a usual additive probability space or on an additive space can be obtained as a copula of its margins meaning that its possible extraordinariness depends solely on its margins this might indicate that copulas are a stronger probability concept than probability itself

on the degree of asymmetry of a quasi copula with respect to a curve abstract the geometrical interpretation of symmetry of a function on the unit square is that it takes the same value in mirror images w r t the main diagonal here this concept is generalized by considering the reflection w r t a curve representing the graph of an automorphism of the unit interval a function on the unit square that takes the same value in mirror images w r t such a curve is called symmetric w r t that curve moreover a measure is proposed for quantifying to what extent a quasi copula can be regarded as being asymmetric w r t a given curve the major part of the paper is concerned with establishing lower and upper bounds on this degree of asymmetry finally it is shown that these bounds are sharp within the class of copulas

aperiodic ising model on the bethe lattice exact results we consider the ising model on the bethe lattice with aperiodic modulation of the couplings which has been studied numerically in phys rev e 77 041113 2008 here we present a relevance irrelevance criterion and solve the critical behavior exactly for marginal aperiodic sequences we present analytical formulas for the continuously varying critical exponents and discuss a relationship with the surface critical behavior of the aperiodic quantum ising chain

quasi copulas and signed measures we study the relationship between multivariate quasi copulas and measures that they may or may not induce on 0 1 n we first study the mass distribution of the pointwise best possible lower bound for the set of n quasi copulas for n 3 as a consequence we show that not every n quasi copula induces a signed measure on 0 1 n

binary survival aggregation functions we introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas a well studied class of binary aggregation functions with a profound probabilistic interpretation to their associated survival copulas the new transformation called double flipping is the composition of two elementary flipping transformations introduced earlier each operating on one of the arguments of the aggregation function we lay bare the relationships between these elementary flipping operations and double flipping we study invariants under these transformations furthermore we characterize the transformations that preserve flippability most importantly we characterize different subclasses of flippable aggregation functions in particular aggregation functions that have an absorbing element or that have a neutral element in this investigation the key role played by quasi copulas and their dual operations is highlighted these findings support the introduction of the term survival aggregation function

rapid reanalysis of the generalized eigenvalue problem of locally modified linear dynamical systems abstract a computationally efficient method for the reanalysis of the damped generalized eigenvalue problems associated with linear dynamical systems with local damping and stiffness modifications is developed no restrictions are imposed on the damping of the system and the modifications in the damping and the stiffness can be independent of each other the application of the developed method to the undamped generalized eigenvalue problem with mass and stiffness modifications is also discussed the proposed method achieves up to three orders of magnitude gains in computational efficiency compared to the conventional solution procedures

eigenvalue error analysis of viscously damped structures using a ritz reduction method the efficient solution of the eigenvalue problem that results from inserting passive dampers with variable stiffness and damping coefficients into a structure is addressed eigenanalysis of reduced models obtained by retaining a number of normal modes augmented with ritz vectors corresponding to the static solutions resulting from the load patterns introduced by the dampers has been empirically shown to yield excellent approximations to the full eigenvalue problem an analysis of this technique in the case of a single damper is presented a priori and a posteriori error estimates are generated and tested on numerical examples comparison theorems with modally truncated models and a markov parameter matching reduced order model are derived these theorems corroborate the heuristic that residual flexibility methods improve low frequency approximation of the system the analysis leads to other techniques for eigenvalue approximation approximate closed form solutions are derived that include a refinement to eigenvalue derivative methods for approximation an efficient newton scheme is also developed a numerical example is presented demonstrating the effectiveness of each of these methods