waves and bumps in neuronal networks with axo dendritic synaptic interactions we consider a firing rate model of a neuronal network continuum that incorporates axo dendritic synaptic processing and the finite conduction velocities of action potentials the model equation is an integral one defined on a spatially extended domain apart from a spatial integral mixing the network connectivity function with space dependent delays arising from non instantaneous axonal communication the integral model also includes a temporal integration over some appropriately identified distributed delay kernel these distributed delay kernels are biologically motivated and represent the response of biological synapses to spiking inputs they are interpreted as green s functions of some linear dierential operator exploiting this green s function description we discuss formal reductions of this non local system to equivalent partial dierential equation pde models we distinguish between those spatial connectivity functions that give rise to local pde models and those that give rise to pde models with delayed non local terms for cases in which local pdes are derived we investigate traveling wave solutions in a comoving frame by numerically computing global heteroclinic connections for sigmoidal firing rate functions we also calculate exact solutions parameterized by axonal conduction velocity for the heaviside firing rate function the sigmoidal firing rate function in the limit of infinte gain the inclusion of synaptic adaptation is shown to alter traveling wave fronts to traveling pulses which we study analytically and numerically in terms of a global homoclinic orbit finally we consider the impact of dendritic interactions on waves and on static spatially localized solutions exact analysis for

general chebyshev type inequalities for universal integral a new inequality for the universal integral on abstract spaces is obtained in a rather general form as two corollaries minkowski s and chebyshev s type inequalities for the universal integral are obtained the main results of this paper generalize some previous results obtained for special fuzzy integrals e g choquet and sugeno integrals furthermore related inequalities for seminormed integral are obtained

localized turing patterns in nonlinear optical cavities abstract the subcritical turing instability is studied in two classes of models for laser driven nonlinear optical cavities in the first class of models the nonlinearity is purely absorptive with arbitrary intensity dependent losses in the second class the refractive index is real and is an arbitrary function of the intracavity intensity through a weakly nonlinear analysis a ginzburg landau equation with quintic nonlinearity is derived thus the maxwell curve which marks the existence of localized patterns in parameter space is determined in the particular case of the lugiato lefever model the analysis is continued to seventh order yielding a refined formula for the maxwell curve and the theoretical curve is compared with recent numerical simulation by gomila et al d gomila a scroggie w firth bifurcation structure of dissipative solitons physica d 227 2007 70 77

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

nonlinearity of the fuzzy integral we prove that the fuzzy integral has some linearity properties only for small classes of fuzzy measures we also show that an extension of this concept to bounded functions as proposed by kandel 2 5 is not well defined in general

periodic solutions of some infinite dimensional hamiltonian systems associated with non linear partial difference equations ii this is our second paper devoted to the study of some non linear schrodinger equations with random potential we study the non linear eigenvalue problems corresponding to these equations we exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails contrary to our results in the first paper the results established in the present paper hold for an arbitrary strength of the non linear cubic term in the non linear schrodinger equation

successive homoclinic tangencies to a limit cycle the dynamics near a perturbed degenerate homocfinic connection to a periodic orbit in three dimensions is modeled by a two parameter map one parameter controls the passage of the manifolds of the orbit through one another and the other breaks the degeneracy and causes the manifolds to intersect transversely an analysis of the map recovers the results of gaspard and wang 1987 relating to the accumulation of saddle node bifurcations of periodic orbits on a single homoclinic tangency and in addition shows that the local behavior of these orbits at the two tangencies can be linked together giving closed loops in period versus parameter plots these analytic results are then compared with numerical results from a three dimensional of ordinary differential equations

statistical analysis of parametric t norms theoretical aspects of aggregation functions particularly t norms have been deeply investigated a further step in the study of these functions is to consider statistical behavior of outputs this research approach has been initiated by the authors in a recent paper mainly focused on the compensatory functions such as averages now parametric t norms are especially studied in order to provide simply easy rules to be used by practitioners when choosing one parameter value a pairwise parametric comparison of several t norm families is provided by means of charts

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

schrodinger operator with a nonlocal potential whose absolutely continuous and point spectra coexist we consider the schrodinger like operatorh in which the role of a potential is played by the lattice sum of rank 1 operators left v n right rangle left langle v n right multiplied by g tan n g 0 d n d 0 1 we show that if the vector satisfies the diophantine condition and the fourier transform support of the functionsv n x v x n x d n d is small then the spectrum ofh consists of a dense point component coinciding with and an absolutely continuous component coinciding with where is the radius of the mentioned support besides we find the integrated density of statesn it has a jump at and zero temperature a c conductivity v that also has a jump at and vanishes faster than any power of the external field frequency as 0 and

general barnes godunova levin type inequalities for sugeno integral integral inequalities play important roles in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure for instance in decision theory the sugeno integral is a median which is indeed a qualitative counterpart to the averaging operation underlying expected utility in this paper barnes godunova levin type inequalities for the sugeno integral on abstract spaces are studied in a rather general form and for this we introduce some new technics for the treatment of concave functions in the sugeno integration context also several examples are given to illustrate the validity of this inequality moreover a strengthened version of barnes godunova levin type inequality for sugeno integrals on a real interval based on a binary operation is presented

generalizations of the chebyshev type inequality for choquet like expectation this paper proves generalizations of the chebyshev type inequality for choquet like expectation some previous results are obtained as corollaries

newton s method and periodic solutions of nonlinear wave equations we prove the existence of periodic solutions of the nonlinear wave equation satisfying either dirichlet or periodic boundary conditions on the interval o the coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation using a version of newton s method we show that this equation has solutions provided the nonlinearity g x u satisfies certain generic conditions of nonresonance and genuine nonlinearity 1993 john wiley sons inc

localization length of stationary states in the nonlinear schrodinger equation for the nonlinear schrodinger equation nlse in the presence of disorder exponentially localized stationary states are found we demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation the analysis makes use of the correspondence between the stationary nlse and the langevin equation as well as of the resulting fokker planck equation the calculations are performed for the white noise random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically it is argued that the main conclusions are robust

the static deformation of a twisted elastic rod constrained to lie on a cylinder the cosserat director theory is used to formulate the problem of a long thin weightless rod constrained by suitable distributed forces to lie on a cylinder while being held by end tension and twisting moment applications of this problem are found for instance in the buckling of drill strings inside a cylindrical hole in the case of a rod of isotropic cross section the equilibrium equations can be reduced to those of a one degree of freedom oscillator in terms of the angle that the local tangent to the rod makes with the axis of the cylinder depending on the radius of the cylinder and the applied load the oscillator has several fixed points each of which corresponds to a different helical solution of the rod more complicated shapes are also possible and special attention is given to localized configurations described by homoclinic orbits of the oscillator heteroclinic saddle connections are found to play an important role in the post buckling behaviour by defining critical loads at which a straight rod may coil up into a helix

heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible hamiltonian hopft bifurcation this paper considers an unfolding of a degenerate reversible 1 1 resonance or hamiltonian hopf bifurcation for four dimensional systems of time reversible ordinary differential equations odes this bifurcation occurs when a complex quadruple of eigenvalues of an equilibrium coalesce on the imaginary axis to become imaginary pairs the degeneracy occurs via the vanishing of a normal form coefficient q2 0 that determines whether the bifurcation is super or subcritical of particular concern is the behaviour of homoclinic and heteroclinic connections between the trivial equilibrium and simple periodic orbits a partial unfolding of such solutions already occurs in the work of dias and iooss eur j mech b fluids 15 1996 367 393 given a sign of the coefficient of a higher order term q4 0 and 1 q2 0 the normal form then shows a small amplitude bifurcating branch of homoclinic solutions terminating at a heteroclinic connection to a simple periodic orbit a genericity argument shows that this connection is not structurally stable and should break into a pair of heteroclinic tangencies this is confirmed by numerics which shows that branches of the simplest homoclinic orbits undergo an infinite snaking sequence of limit points accumulating on the parameter values of the two tangencies at each limit point the homoclinic orbit generates another bump close to the periodic orbit as q2 is further decreased from zero the snake widens until at a critical value a branch is formed of heteroclinic connections from the origin to a nontrivial equilibrium a kink for q2 less than this value the kinks heteroclinic tangencies and snake like curves no longer occur

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

triangular norms position paper iii continuous t norms this third and last part of a series of position papers on triangular norms for parts i and ii see e p klement r mesiar e pap triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press e p klement r mesiar e pap triangular norms position paper ii general constructions and parameterized families submitted for publication presents the representation of continuous archimedean t norms by means of additive generators and the representation of continuous t norms by means of ordinal sums with archimedean summands both with full proofs finally some consequences of these representation theorems in the context of comparison and convergence of continuous t norms and of the determination of continuous t norms by their diagonal sections are mentioned

distributivity inequalities of monotonic operations the aim of this work is to complement recent results about distributive binary operations our investigation was motivated by non distributive logical connectives and their generalizations in fuzzy set theory in spite of the title we neither solve the concerned functional inequalities nor look for characterization of the solutions of such inequalities we only lay bare conditions for their fulfilment for monotonic operations with neutral or zero element we present the sufficient conditions to obtain the subdistributivity or superdistributivity in the case of the lack of distributivity for the considered pairs of operations in particular we describe families of increasing binary operations subdistributive or superdistributive with respect to idempotent uninorms and nullnorms

homoclinic and heteroclinic orbits underlying the post buckling of axially compressed cylindrical shells abstract a structural system with an unstable post buckling response that subsequently restabilizes has the potential to exhibit homoclinic connections from the fundamental equilibrium state to itself over a range of loads and heteroclinic connections between fundamental and periodic equilibrium states over a different smaller range of loads it is argued that such equilibrium configurations are important in the interpretation of observed behaviour and govern the minimum possible post buckling loads to illustrate this the classical problem of a long thin axially compressed cylindrical shell is revisited from three different perspectives asymptotic conjecture analogy with nonlinear dynamics and numerical continuation analysis of a partial spectral decomposition of the underlying equilibrium equations the nonlinear dynamics analogy demonstrates that the structure of the heteroclinic connections is more complicated than that indicated by the asymptotics this is confirmed by the numerics however when the asymptotic portrayal is compared to the numerics it turns out to be surprisingly accurate in its maxwell load prediction of the practically significant first minimum to appear in the post buckling regime

perturbed homoclinic solutions in reversible 1 1 resonance vector fields we consider a smooth reversible vector field in r 4 such that the origin is a fixed point the differential at the origin has two double pure imaginary eigenvalues iq for the critical value 0 of the parameter we show by a normal form analysis that the vector field can be approximated by an integrable field in r 4 for which we know all solutions specially interesting ones are the homoclinics to 0 and homoclinics to periodic solutions depending on the sign of a leading nonlinear coefficient we prove in particular the persistence of these homoclinics for the full vector field

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

periodic and quasi periodic solutions of nonlinear wave equations via kam theory in this paper the nonlinear wave equation u u u xx v x u x t varepsilon u 3 x t 0 is studied it is shown that for a large class of potentials v x one can use kam methods to construct periodic and quasi periodic solutions in time for this equation

quasi copulas with a given sub diagonal section abstract as is well known the frechet hoeffding bounds are the best possible for both copulas and quasi copulas for every quasi copula q max x y 1 0 q x y min x y for all x y 0 1 sharper bounds hold when the quasi copulas take prescribed values e g along their diagonal or horizontal resp vertical sections here we pursue two goals first we investigate construction methods for quasi copulas with a given sub diagonal section i e with prescribed values along the straight line segment joining the points x 0 0 and 1 1 x 0 for x 0 0 1 then we determine the best possible bounds for sets of quasi copulas with a given sub diagonal section

effects of exponentially small terms in the perturbation approach to localized buckling localized buckling solutions are known to exist in the heuristic model of an elastic strut resting on an elastic winkler foundation the primary localized solution emerging from the critical buckling state consists of an amplitude envelope of approximately the form of a hyperbolic secant function which modulates a fast varying sinusoidal oscillation in previous works such solutions have been tracked for the entire post buckling regime both numerically and through a rayleigh ritz approach a very rich structure is known to exist in the subcritical load range but has been proved to exist for only a certain family of reversible systems studies have concentrated on symmetric homoclinic solutions and the asymmetric solutions which bifurcate from these solution paths the primary solution is known to exist for the entire subcritical parameter range and all other symmetric and associated asymmetric solutions exist strictly for values less than critical here we uncover a new family of antisymmetric solutions and some asymptotic analysis suggests that the primary antisymmetric solution exists over the same range as does the primary symmetric solution a perturbation approach can be used so as to describe the bifurcation hierarchy for the novel antisymmetric forms we illustrate a unified approach which is able to predict the circumstances under which non divergent localized solutions are possible and the results of the analysis are compared with some numerical solutions

the distributivity property of increasing binary operations abstract this paper is mainly devoted to solving the functional equations of distributivity and conditional distributivity of increasing binary operations with the unit our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory in particular some assumptions namely associativity and commutativity and results about conditional distributivity of uninorms and triangular norms and triangular conorms were simplified moreover some other properties e g componentwise convexity concavity for special operations from the class of quasi copulas is considered

metrics and t equalities abstract the relationship between metrics and t equalities is investigated the latter are a special case of t equivalences a natural generalization of the classical concept of an equivalence relation it is shown that in the construction of metrics from t equalities triangular norms with an additive generator play a key role conversely in the construction of t equalities from metrics this role is played by triangular norms with a continuous additive generator or equivalently by continuous archimedean triangular norms these results are then applied to the biresidual operator e t of a triangular norm t it is shown that e t is a t equality on 0 1 if and only if t is left continuous furthermore it is shown that to any left continuous triangular norm t there correspond two particular t equalities on f x the class of fuzzy sets in a given universe x one of these t equalities is obtained from the biresidual operator e t t by means of a natural extension procedure these t equalities then give rise to interesting metrics on f x

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

some properties of weak uninorms a weak uninorm is not only a generalization of a uninorm but also of a nullnorm in this paper we will show that if a weak uninorm is archimedean then it is an archimedean nullnorm and if a weak uninorm is e archimedean then it is an archimedean uninorm moreover the de morgan triples of the weak uninorms will be characterized too

a continuation method for nonlinear eigenvalue problems abstract in this note we present a theorem which turns out to be a useful tool to prove the existence of solutions of nonlinear eigenvalue problems we work in an abstract setting and describe shortly an application of this technique the applications worked out so far concern problems of solid state physics related to the theory of localization with interacting electrons

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

the dominance relation in some families of continuous archimedean t norms and copulas the dominance relation in several families of continuous archimedean t norms and copulas is investigated on the one hand the contribution provides a comprehensive overview on recent conditions and properties of dominance as well as known results for particular cases of families on the other hand it contains new results clarifying the dominance relationship in five additional families of continuous archimedean t norms and copulas

anderson localization for multi dimensional systems at large disorder or large energy we prove that discrete schrodinger operators on d with a random potential have almost surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy this is the first proof of localization for multi dimensional anderson models

dominance on strict triangular norms and mulholland inequality abstract this paper is devoted to the question of transitivity of the dominance relation defined on the set of strict triangular norms and to the connection between dominance and mulholland inequality a summary of the results reached in this field is given and a new result for the strict triangular norms of family 19 is shown further some parametric classes of solutions of mulholland inequality that do not comply with the mulholland s condition are presented and finally it is shown that the dominance relation is in general not transitive on the set of strict triangular norms

nonmonotonic reasoning conditional objects and possibility theory abstract this short paper relates the conditional object based and possibility theory based approaches for reasoning with conditional statements pervaded with exceptions to other methods in nonmonotonic reasoning which have been independently proposed namely lehmann s preferential and rational closure entailments which obey normative postulates the infinitesimal probability approach and the conditional modal logics based approach all these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge although they are based on different modeling frameworks it thus provides a unified understanding of nonmonotonic consequence relations more particularly conditional objects a purely qualitative counterpart to conditional probabilities offer a very simple semantics based on a 3 valued calculus for the preferential entailment while in the purely ordinal setting of possibility theory both the preferential and the rational closure entailments can be represented

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

cellular buckling from mode interaction in i beams under uniform bending beams made from thin walled elements while very efficient in terms of the structural strength and stiffness to weight ratios can be susceptible to highly complex instability phenomena a nonlinear analytical formulation based on variational principles for the ubiquitous i beam with thin flanges under uniform bending is presented the resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post buckling range can be portrayed the interaction between global lateral torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling snaking being predicted theoretically for the first time solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling

on the problem of dynamical localization in the nonlinear schrodinger equation with a random potential we prove a dynamical localization in the nonlinear schrodinger equation with a random potential for times of the order of o 2 w here is the strength of the nonlinear ity

on the joint distribution of energy levels of random schrodinger operators we consider operators with random potentials on graphs such as the lattice version of the random schrodinger operator the main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct intervals with the corresponding eigenfunctions being separately localized within prescribed regions the bound generalizes the wegner estimate on the density of states the analysis proceeds through a new multi parameter spectral averaging principle

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

perturbation theory for periodic orbits in a class of infinite dimensional hamiltonian systems we consider a class of hamiltonian systems describing an infinite array of coupled anharmonic oscillators and we study the bifurcation of periodic orbits off the equilibrium point the family of orbits we construct can be parametrized by their periods which belong to cantor sets of large measure containing certain periods of the linearized problem as accumulation points the infinitely many holes forming a dense set on which the existence of a periodic orbit cannot be proven originate from a dense set of resonances that are present in the system we also have a result concerning the existence of solutions of arbitrarily large amplitude

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

quasi conjunction quasi disjunction t norms and t conorms probabilistic aspects we make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning in a coherence based setting we study the extensions of a probability assessment defined on n conditional events to their quasi conjunction and by exploiting duality to their quasi disjunction the lower and upper bounds coincide with some well known t norms and t conorms minimum product lukasiewicz and hamacher t norms and their dual t conorms on this basis we obtain quasi and and quasi or rules these are rules for which any finite family of conditional events p entails the associated quasi conjunction and quasi disjunction we examine some cases of logical dependencies and we study the relations among coherence inclusion for conditional events and p entailment we also consider the or rule where quasi conjunction and quasi disjunction of premises coincide with the conclusion we analyze further aspects of quasi conjunction and quasi disjunction by computing probabilistic bounds on premises from bounds on conclusions finally we consider biconditional events and we introduce the notion of an n conditional event then we give a probabilistic interpretation for a generalized loop rule in an appendix we provide explicit expressions for the hamacher t norm and t conorm in the unitary hypercube

unitary dressing transformations and exponential decay below threshold for quantum spin systems parts i and ii this is the continuation of a series of articles concerning a class of quantum spin systems with hamiltonian operators of the form h lambda sum limits x in lambda s x sum limits yo subset lambda lambda left yo right c 1 t yo where is a graph is a small parameter andsx has a gap 1 for all x e i in the singular seti the gap ofsx can be arbitrarily small part iii is devoted to the proof of a preliminary result while in part iv we consider the case in whichi is a subset of finite density of this completes the first iteration step of the deterministic part of the proof of localization in the ground state of the random field quantumxy model

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

archimedean overlap functions the ordinal sum and the cancellation idempotency and limiting properties abstract overlap functions are a particular type of aggregation functions given by increasing continuous commutative bivariate functions defined over the unit square satisfying appropriate boundary conditions overlap functions are applied mainly in classification problems image processing and in some problems of decision making based on some kind of fuzzy preference relations in which the associativity property is not strongly required moreover the class of overlap functions is reacher than the class of t norms concerning some properties like idempotency homogeneity and mainly the self closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap functions this flexibility of overlap functions increases their applicability the aim of this papers is to introduce the concept of archimedean overlap functions presenting a study about the cancellation idempotency and limiting properties and providing a characterization of such class of functions the concept of ordinal sum of overlap functions is also introduced providing constructing representing methods of certain classes of overlap functions related to idempotency cancellation limiting and archimedean properties

anderson localization for time quasi periodic random schrodinger and wave equations we prove that at large disorder with large probability and for a corresponding set of diophantine frequencies of large measure anderson localization in d is stable under localized time quasi periodic perturbations by proving that the associated quasi energy operator has pure point spectrum the main tools are the frohlich spencer mechanism for the random component and the bourgain goldstein schlag mechanism for the quasi periodic component this paper paves the way for the construction of time quasi periodic kam type of solutions of non linear random schrodinger equations in bw

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

preservation of fuzzy relation properties based on fuzzy conjunctions and disjunctions during aggregation process in this contribution necessary and sufficient conditions for n argument functions to preserve properties of fuzzy relations during aggregation process are presented the proposed properties depend on binary operations including t norms and t conorms and more generally fuzzy conjunctions and disjunctions generalizations of the following properties are studied antisymmetry asymmetry connectedness transitivity negative transitivity semitransitivity and ferrers property

homoclinic orbits in reversible systems and their applications in mechanics fluids and optics abstract this survey article reviews the theory and application of homoclinic orbits to equilibria in reversible continuous time dynamical systems where the homoclinic orbit and the equilibrium are both reversible the focus is on even order reversible systems in four or more dimensions local theory generic argument and global existence theories are examined for each qualitatively distinct linearisation several recent results such as coalescence caused by non transversality and the reversible orbit flip bifurcation are covered a number of open problems are highlighted applications are reviewed to systems arising from a variety of disciplines with the aid of numerical methods three examples are presented in detail one of which is infinite dimensional

anomalous thermostat and intraband discrete breathers abstract we investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice including quenched disorder the coupling between both parts is bilinear elimination of the harmonic degrees of freedom leads to a nonlinear langevin equation with memory kernels t and noise term t for the anharmonic coordinates q t q t for zero temperature i e for t 0 we prove that the support of the fourier transform of t and of the time averaged velocity velocity correlation functions k t of the anharmonic system cannot overlap as a consequence the asymptotic solutions can be constant periodic quasiperiodic or almost periodic and possibly weakly chaotic for a sinusoidal trajectory q t with frequency we find that the energy e t transferred to the harmonic system up to time t is proportional to t if equals one of the phonon frequencies it is 2 we prove that there is a zero measure set l such that for in its full measure complement r l it is 0 i e there is no energy dissipation under certain conditions l contains a subset l such that for l the dissipation rate is nonzero and may be subdissipative 0 1 or superdissipative 1 2 compared to ordinary dissipation 1 consequently the harmonic bath does act as an anomalous thermostat in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation forcing convergence to equilibrium intraband discrete breathers are such solutions which do not relax we prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a cantor set c k of finite lebesgue measure this is achieved by estimating the contribution of small denominators appearing for g t related to t for c k the small denominators do not lead to divergencies such that g t is a smooth and bounded function in t

subdistributivity and superdistributivity of binary operations recently the property of distributivity of binary operations on 0 1 is of great interest both for practical as well as fundamental reasons in this paper we summarize some facts connected with distributivity and non distributivity of binary operations on 0 1 motivated by non distributive logical connectives in fuzzy set theory we show some new results concerning the above property a new direction of investigations mainly concerns the distributivity inequalities for triangular norms and conorms and their diverse generalizations in particular we look for examples of binary operations fulfilling the distributivity inequalities

asymptotic localization of stationary states in the nonlinear schrodinger equation the mapping of the nonlinear schrodinger equation with a random potential on the fokker planck equation is used to calculate the localization length of its stationary states the asymptotic growth rates of the moments of the wave function and its derivative for the linear schrodinger equation in a random potential are computed analytically and resummation is used to obtain the corresponding growth rate for the nonlinear schrodinger equation and the localization length of the stationary states

towards a general class of operators for fuzzy systems our starting point is the multiplicative utility function which is extensively used in the theory of multicriteria decision making its associativity is shown and as its generalization a class of operators is introduced with fine and useful properties as in special cases it reduces to well known operators of fuzzy set theory min max product einstein hamacher dombi and drastic as a consequence we generalize the addition of velocities in einstein s special relativity theory to multiple moving objects also a new form of the hamacher operator is given which makes multiargument calculations easier we examine the de morgan identity which connects the conjunctive and disjunctive operators by a negation it is shown that in some special cases min max drastic and dombi the operator class forms a de morgan triple with any involutive negation

spatially complex localisation in twisted elastic rods constrained to a cylinder abstract we consider the problem of a long thin weightless rod constrained to lie on a cylinder while being held by end tension and twisting moment applications of this problem are found for instance in the buckling of drill strings inside a cylindrical hole in a previous paper the general geometrically exact formulation was given and the case of a rod of isotropic cross section analysed in detail it was shown that in that case the static equilibrium equations are completely integrable and can be reduced to those of a one degree of freedom oscillator whose non trivial fixed points correspond to helical solutions of the rod a critical load was found where the rod coils up into a helix here the anisotropic case is studied it is shown that the equations are no longer integrable and give rise to spatial chaos with infinitely many multi loop localised solutions helices become slightly modulated we study the bifurcations of the simplest single loop solution and a representative multi loop as the aspect ratio of the rod s cross section is varied it is shown how the anisotropy unfolds the coiling bifurcation the resulting post buckling behaviour is of the softening hardening softening type typically seen in the cellular buckling of long structures and can be interpreted in terms of a so called maxwell effective failure load

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

solitary wave interaction phenomena in a strut buckling model incorporating restabilisation the archetypal model of the buckling of a compressed long elastic strut resting on a nonlinear elastic foundation is studied localised buckling is investigated when the foundation has both quadratic and cubic terms which initially destabilise but subsequently restabilise the structure the primary solution can be detected by a double scale perturbation procedure and is reminiscent of a solitary wave essentially it consists of a fast periodic oscillation which is slowly modulated and decays exponentially in both directions particular interest is paid to the process of adapting the procedure to account for the post buckling behaviour of two packet or double humped solitary waves in this model we employ the methods of beyond all orders asymptotics to reveal terms formally exponentially small in the perturbation parameter which have macroscopic effects on the post buckling behaviour of the system including the interaction phenomenon of interest the analysis is reinforced by direct numerical computations which reveal the so called snaking behaviour in the subsidiary homoclinic orbits as is observed in the case of primary solutions however additional phenomena arise for these subsidiary forms including the formation of bridges linking solution paths and the appearance of a multitude of closed isolated loops disconnected from other features of the bifurcation diagram

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

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

asymptotics of cellular buckling close to the maxwell load we study the deformation of an elastic strut on a nonlinear winkler foundation subjected to an axial compressive load p using multi scale analysis and numerical methods we describe the localized cellular post buckled state of the system when p is removed from the critical load p 2 the solutions and their modulation frequencies differ significantly from those predicted by weakly nonlinear analysis very close to p 2 in particular when p approaches the maxwell load pm the localized solutions approach a large amplitude heteroclinic connection between an unbuckled solution and a periodic solution an asymptotic description of pm in terms of the system parameters is given the agreement between the numerical calculations and the asymptotic approximations is striking

inferential processes leading to possibility and necessity this paper deals with the upper and lower bounds of a class of uncertainty measures endowed with particular characteristics decomposability monotonicity partial additivity and so on we consider an initial partial assessment consistent with either probability or possibility or necessity then we study the upper and lower envelopes of all possible extensions by resorting to a notion of weak logical independence we get as lower or upper envelope a possibility or a necessity respectively starting either from a probability or from a possibility or from a necessity

a generalization of the mulholland inequality for continuous archimedean t norms it is well known that dominance between strict t norms is closely related to the mulholland inequality which can be seen as a generalization of the minkowski inequality however strict t norms constitute only one part of the class of continuous archimedean t norms the basic elements from which all continuous t norms are composed in this paper dominance between continuous archimedean t norms is shown to be related to a generalization of the mulholland inequality we provide sufficient and necessary conditions for its fulfillment

probabilistic valued decomposable set functions with respect to triangle functions real world applications often require dealing with the situations in which the exact numerical values of the sub measure of a set may not be provided but at least some probabilistic assignment still could be done also several concepts in uncertainty processing are linked to the processing of distribution functions in the framework of generalized measure theory we introduce the probabilistic valued decomposable set functions which are related to triangle functions as natural candidates for the addition in an appropriate probabilistic metric space several set functions among them the classical sub measures previously defined t submeasures l a submeasures as well as recently introduced shen s sub measures are described and investigated in a unified way basic properties and characterizations of decomposable sub measures are also studied and numerous extensions of results from the above mentioned papers are provided

orthogonal grid constructions of copulas we establish a general framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with nonoverlapping rectangles as patches we derive a family of construction methods that require the choice of a single background copula when this background copula is the greatest copula we retrieve the well known ordinal sum construction while in the case of the smallest copula we obtain a construction method that is dual to the ordinal sum construction also nonsingular background copulas lead to suitable construction methods

bifurcation analysis to the lugiato lefever equation in one space dimension we study the stability and bifurcation of steady states for a certain kind of damped driven nonlinear schrodinger equation with cubic nonlinearity and a detuning term in one space dimension mathematically in a rigorous sense it is known by numerical simulations that the system shows lots of coexisting spatially localized structures as a result of subcritical bifurcation since the equation does not have a variational structure unlike the conservative case we cannot apply a variational method for capturing the ground state hence we analyze the equation from a viewpoint of bifurcation theory in the case of a finite interval we prove the fold bifurcation of nontrivial stationary solutions around the codimension two bifurcation point of the trivial equilibrium by exact computation of a fifth order expansion on a center manifold reduction in addition we analyze the steady state mode interaction and prove the bifurcation of mixed mode solutions which will be a germ of localized structures on a finite interval finally we study the corresponding problem on the entire real line by use of spatial dynamics we obtain a small dissipative soliton bifurcated adequately from the trivial equilibrium

dominance in the family of sugeno weber t norms the dominance relationship between two members of the family of sugeno weber t norms is proven by using a quantifier elimination algorithm further it is shown that dominance is a transitive and therefore also an order relation on this family of t norms

on a certain class of aggregative operators abstract here our starting point is a study of connection with dombi aggregative operators uninorms strict t norms and t conorms we present a new representation theorem of strong negations that explicitly contains the neutral value then the relationships for aggregative operators and strong negations are verified as well as those for the t norm and t conorm using the pan operator concept we introduce the multiplicative pliant concept and give the necessary and sufficient conditions for it we study a certain class of weighted aggregative operators representable uninorms which build a self demorgan class with infinitely many negations we provide the necessary and sufficient conditions for these operators

non linear wave and schrodinger equations i instability of periodic and quasiperiodic solutions we investigate stability of periodic and quasiperiodic solutions of linear wave and schrodinger equations under non linear perturbations we show in the case of the wave equations that such solutions are unstable for generic perturbations for the schrodinger equations periodic solutions are stable while the quasiperiodic ones are not we extend these results to periodic solutions of non linear equations

exponential asymptotics of localised patterns and snaking bifurcation diagrams abstract localised patterns emerging from a subcritical modulation instability are analysed by carrying the multiple scales analysis beyond all orders the model studied is the swift hohenberg equation of nonlinear optics which is equivalent to the classical swift hohenberg equation with a quadratic and a cubic nonlinearity applying the asymptotic technique away from the maxwell point first it is shown how exponentially small terms determine the phase of the fast spatial oscillation with respect to their slow sech type amplitude in the vicinity of the maxwell point the beyond all orders calculation yields the pinning range of parameters where stable stationary fronts connect the homogeneous and periodic states the full bifurcation diagram for localised patterns is then computed analytically including snake and ladder bifurcation curves this last step requires the matching of the periodic oscillation in the middle of a localised pattern both with an up and a down front to this end a third super slow spatial scale needs to be introduced in which fronts appear as boundary layers in addition the location of the maxwell point and the oscillation wave number of localised patterns are required to fourth order accuracy in the oscillation amplitude