lesche stability of κ entropy abstract the lesche stability condition for the shannon entropy j stat phys 27 1982 419 represents a fundamental test for its experimental robustness for systems obeying the maxwell boltzmann statistical mechanics of course this stability condition must be satisfied by any entropic functional candidate to generate non conventional statistical mechanics in the present effort we show that the entropy recently introduced in literature phys rev e 66 2002 056125 satisfies the lesche stability condition

on the number of limit cycles for a class of discontinuous quadratic differential systems abstract the present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center x y 16 3 x 2 4 3 y 2 y x 8 3 x y by the averaging method of first order when it is perturbed inside a class of discontinuous quadratic polynomial differential systems the chebyshev criterion is used to show that this maximum number is 5 and can be realizable in some sense the result and that in paper 6 also answer the questions left in the paper 9

order equivalent triangular norms in this paper an equivalence relation on the class of t norms induced by a t partial order is provided and discussed the equivalence classes linked to some special t norms are characterized as well as some properties preserved by the introduced equivalence defining the set of incomparable elements with respect to the t partial order this set is deeply investigated finally we give an answer to a recently posed open problem

modelling of income distribution in the european union with the fokker planck equation abstract herein we applied statistical physics to study incomes of three low medium and high income society classes instead of the two low and medium income classes studied so far in the frame of the threshold nonlinear langevin dynamics and its threshold fokker planck counterpart we derived a unified formula for description of income of all society classes by way of example of those of the european union in years 2006 and 2008 hence the formula is more general than the well known formula of yakovenko et al that is our formula well describes not only two regions but simultaneously the third region in the plot of the complementary cumulative distribution function vs an annual household income furthermore the known stylised facts concerning this income are well described by our formula namely the formula provides the boltzmann gibbs income distribution function for the low income society class and the weak pareto law for the medium income society class as expected importantly it predicts to satisfactory approximation the zipf law for the high income society class moreover the region of medium income society class is now distinctly reduced because the bottom of high income society class is distinctly lowered this reduction made in fact the medium income society class an intermediate income society class

limit cycles of a lienard system with symmetry allowing for discontinuity abstract this paper presents new results on the limit cycles of a lienard system with symmetry allowing for discontinuity our results generalize and improve the results in 32 theorem 1 and 2 or the monograph 33 chapter 4 theorem 5 2 the results in 33 are only valid for the smooth system we emphasize that our main results are valid for discontinuous systems moreover we show the presence and an explicit upper bound for the amplitude of the two limit cycles and we estimate the position of the double limit cycle bifurcation surface in the parameter space until now there is no result to determine the amplitude of the two limit cycles the existing results on the amplitude of limit cycles guarantee that the lienard system has a unique limit cycle finally some applications and examples are provided to show the effectiveness of our results we revisit a co dimension 3 lienard oscillator see 22 34 in application 1 li and rousseau 22 studied the limit cycles of such a system when the parameters are small however for the general case of the parameters in particular the parameters are large the upper bound of the limit cycles remains open we completely provide the bifurcation diagram for the one equilibrium case moreover we determine the amplitude of the two limit cycles and estimate the position of the double limit cycle bifurcation surface for the one equilibrium case application 2 is presented to study the limit cycles of a class of the filippov system

infinitely distributive t norms on complete lattices and pseudo complements in this paper we have introduced the concepts of t prime element t prime radical element and t semi prime element and have studied their properties we have investigated the construction methods of new infinitely distributive t norms from given infinitely distributive t norms by means of t prime elements and pseudo complements if every element of l is t prime radical element then we show that l is a complete brouwerian lattice and email protected if l is an algebraic lattice t is a t norm on l and every compact element of l is idempotent then we obtain that email protected we show that l r is a complete lattice and that the restriction of t to l r is an infinitely distributive t norm on l r when t is an infinitely distributive t norm on l and 0 is a t prime we present infinitely distributive t norms on a complete sublattice l and study their properties

on ordinal sums of triangular norms on bounded lattices ordinal sums have been introduced in many different contexts e g for posets semigroups t norms copulas aggregation operators or quite recently for hoops in this contribution we focus on ordinal sums of t norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets necessary and sufficient conditions are provided for an ordinal sum operation yielding again a t norm on some bounded lattice whereas the operation is determined by an arbitrary selection of subintervals as carriers for arbitrary summand t norms by such also the structure of the underlying bounded lattice is investigated further it is shown that up to trivial cases there are no ordinal sum t norms on product lattices in general

characterizing when an ordinal sum of t norms is a t norm on bounded lattices one of the most important operators in soft computing are the triangular norms t norms as well as the combination among them the ordinal sum of triangular norms on 0 1 has been used to construct other triangular norms however on a bounded lattice an ordinal sum of t norms may not be a t norm several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t norms is in fact a t norm moreover we show that a large set of ordinal sums verify these conditions hence they are very interesting in order to verify whether an ordinal sum on a bounded lattice is a t norm for a particular family of t norms

the κ generalized distribution a new descriptive model for the size distribution of incomes this paper proposes the generalized distribution as a model for describing the distribution and dispersion of income within a population formulas for the shape moments and standard tools for inequality measurement such as the lorenz curve and the gini coefficient are given a method for parameter estimation is also discussed the model is shown to fit extremely well the data on personal income distribution in australia and in the united states c 2008 elsevier b v all rights reserved

medians and nullnorms on bounded lattices nullnorms are generalizations of triangular norms and triangular conorms with a zero element in the interior of the unit interval in this paper we work on nullnorms which are defined on an arbitrary bounded lattice we introduce a general median based method for constructing nullnorms by means of triangular norms and triangular conorms furthermore we highlight a significant difference between the existence and representation of idempotent nullnorms on chains distributive bounded lattices and general bounded lattices

bounding the number of zeros of certain abelian integrals abstract in this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n abelian integrals to have at most n k 1 zeros counted with multiplicities this condition involves the functions in the integrand of the abelian integrals and it can be checked in many cases in a purely algebraic way

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

a study of the personal income distribution in australia we analyze the data on personal income distribution from the australian bureau of statistics we compare fits of the data to the exponential log normal and gamma distributions the exponential function gives a good albeit not perfect description of 98 of the population in the lower part of the distribution the log normal and gamma functions do not improve the fit significantly despite having more parameters and mimic the exponential function we find that the probability density at zero income is not zero which contradicts the log normal and gamma distributions but is consistent with the exponential one the high resolution histogram of the probability density shows a very sharp and narrow peak at low incomes which we interpret as the result of a government policy on income redistribution r 2006 elsevier b v all rights reserved

bifurcation of limit cycles from quadratic isochrones abstract for a one parameter family of plane quadratic vector fields x e depending analytically on a small real parameter e we determine the number and position of the local families of limit cycles which emerge from the periodic trajectories surrounding an isochronous or linearizable center techniques are developed for treating the bifurcations of all orders and these are applied to prove the following results for the linear isochrone the maximum number of continuous families of limit cycles which can emerge is three for one class of nonlinear isochrones at most one continuous family of limit cycles can emerge whereas for all other nonlinear isochrones at most two continuous families of limit cycles can emerge moreover for each isochrone in one of these classes there are small perturbations such that the indicated maximum number of continuous families of limit cycles can be made to emerge from a corresponding number of arbitrarily prescribed periodic orbits within the period annulus of the isochronous center

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

distributive n ary semicopulas on lattices in the present paper definitions of an n ary semicopula on a bounded lattice l a distributive n ary semicopula on l and an infinite distributive n ary semicopula on l are introduced a relation between the set of all bounded lattices l with a distributive n ary semicopula on l and the set of all bounded lattices l with a distributive m ary semicopula on l where 2 n 2 m n m is obtained the method is given for investigation of the following questions a description of all bounded lattices l such that every n ary semicopula on l is distributive and a description of all complete lattices l such that every n ary semicopula on l is infinite distributive

oscillations in the tsallis income distribution abstract oscillations in the complementary cumulative distribution function ccdf of individual income data have been found in the data of various countries studied by different authors at different time periods but the dynamical origins of this behavior are currently unknown although these datasets can be fitted by different functions at different income ranges the tsallis distribution has recently been found capable of fitting the whole distribution by means of only two parameters this procedure showed clearly such oscillatory feature in the entire income range feature but made it particularly visible at the tail of the distribution although log periodic functions fitted to the data are capable of describing this behavior a different approach to naturally disclose such oscillatory characteristics is to allow the tsallis q parameter to become complex in this paper we use this idea in order to describe the behavior of the ccdf of the brazilian personal income recently studied empirically by soares et al 2016 typical elements of periodic motion such as amplitude and angular frequency coupled to this income analysis were obtained by means of this approach a highly non linear function for the ccdf was obtained through this methodology and a numerical test showed it capable of recovering the main oscillatory feature of the original ccdf of the personal income data of brazil

a general method for constructing left continuous t norms a new method for constructing left continuous t norms is introduced and analyzed in this paper we shall construct via embedding a left continuous t norm from any countable residuated totally and densely ordered commutative integral monoid moreover we can construct a left continuous t norm from any countable totally ordered commutative integral monoid which is not necessarily densely ordered and residuated a special case the embedding of such monoids on lexicographic product spaces is investigated in detail and several examples are demonstrated the results shed some light to chang s mv algebra to a recently proposed extraordinary t norm and to the standard semantics of the recently introduced logic ii mtl of hajek

an order induced by nullnorms and its properties abstract in this paper an order induced by nullnorms on bounded lattices is given and discussed we define the set of incomparable elements with respect to the order induced by a nullnorm also by defining such an order an equivalence relation on the class of nullnorms is defined and this equivalence is deeply investigated

semi t operators on bounded lattices abstract we study semi t operators on bounded lattices and show the existence of semi t operators using the fact that there exist some pseudo t norms and pseudo t conorms on the arbitrary fixed bounded lattice l as a by product some constructive approaches to semi t operators are discussed using these approaches we obtain the least semi t operators and the greatest semi t operators on bounded lattices a partial order relation is also defined based on the semi t operator and some properties of this relation are examined

limit cycles for discontinuous quadratic differential systems with two zones abstract in this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems which can bifurcate from the periodic orbits of the quadratic isochronous centers x y x 2 y x x y and x y x 2 y 2 y x 2 x y when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y 0 comparing the obtained results for the discontinuous with the results for the continuous quadratic polynomial differential systems this work shows that the discontinuous systems have at least 3 more limit cycles surrounding the origin than the continuous ones

on the direct decomposability of pseudo t norms t norms and implication operators on product lattices in this paper we discuss the direct decomposability of pseudo t norms and t norms on a product lattice characterize the implication operator on a product lattice that is a direct product of two implication operators and study the direct decomposability of s implications r implications n reciprocal r implications and n reciprocal ql implications on a product lattice

stabilities of generalized entropies the generalized entropic measure which is maximized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity is considered to examine if it can be of physical relevance its experimental robustness is discussed in particular lesche s criterion is analysed which states that an entropic measure is stable if its change under an arbitrary weak deformation of the distribution representing fluctuations of experimental data remains small it is essential to note the difference between this criterion and thermodynamic stability a general condition under which the generalized entropy becomes stable is derived examples known in the literature including the entropy for the stretched exponential distribution the quantum group entropy and the entropy are discussed

the gompertz pareto income distribution abstract this work analyzes the gompertz pareto distribution gpd of personal income formed by the combination of the gompertz curve representing the overwhelming majority of the economically less favorable part of the population of a country and the pareto power law which describes its tiny richest part equations for the lorenz curve gini coefficient and the percentage share of the gompertzian part relative to the total income are all written in this distribution we show that only three parameters determined by linear data fitting are required for its complete characterization consistency checks are carried out using income data of brazil from 1981 to 2007 and they lead to the conclusion that the gpd is consistent and provides a coherent and simple analytical tool to describe personal income distribution data

on the direct decomposability of strong negations and s implication operators on product lattices in this paper we discuss the direct product of strong negations we characterize strong negations on product lattices that are direct products of strong negations furthermore we present a method for constructing t norms on product lattices which are not direct products this method is quite general and useful to generate a wide class of such t norms and solves an open problem posed in 2003 by jenei and de baets finally we study direct decompositions of s implication operators on product lattices

on the t partial order and properties for a t norm t on 0 1 a partial order t was recently defined and studied in this study for any fixed email protected 0 1 we define the set of incomparable elements according to t and this set is deeply investigated by means of the equivalence relation defined in 14 it is shown the set 0 1 denoting the set of all equivalence classes on t norms on 0 1 is uncountably infinite finally with the help of any t norm t on 0 1 it is obtained that the family t l l 0 1 of t norms on 0 1 if t is a divisible t norm then it is obtained that 0 1 t l is a lattice thus we give an answer to an open problem in 10

internal direct product of integral ν distributive binary aggregation functions and the classification of all integral ν distributive binary aggregation functions of length 3 we present some relations between an external direct product and an internal direct product of a family of integral distributive binary aggregation functions relations between a direct decomposition of the unit and a family of pairwise comaximal elements in a lattice with an integral distributive binary aggregation function are investigated using these results the classification of all integral distributive binary aggregation functions on a lattice of length 3 and a description of all lattices of length 3 with an integral distributive binary aggregation function are given

limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems abstract in this paper we consider the quadratic isochronous centers perturbed inside piecewise polynomial differential systems of arbitrary degree n with the straight line of discontinuity x 0 the main concerns are the number of zeros of the first order melnikov functions and the estimate of the number of limit cycles bifurcating from the period annuli for quadratic isochronous centers s 1 s 2 and s 3 we will provide a sharp upper bound for the number of zeros of the first order melnikov functions for quadratic isochronous center s 4 we give a rough estimate however when the problem is reduced to perturbations inside polynomial differential systems our result for s 4 will improve that in li et al 2000 12 significantly moreover we will reveal out some equivalence between the first order melnikov function method and the first order averaging method for investigating the number of limit cycles of piecewise polynomial differential systems

the power law tail exponent of income distributions abstract in this paper we tackle the problem of estimating the power law tail exponent of income distributions by using the hill s estimator a subsample semi parametric bootstrap procedure minimizing the mean squared error is used to choose the power law cutoff value optimally this technique is applied to personal income data for australia and italy

non linear kinetics underlying generalized statistics abstract the purpose of the present effort is threefold firstly it is shown that there exists a principle that we call kinetical interaction principle kip underlying the non linear kinetics in particle systems independently on the picture kramers boltzmann used to describe their time evolution secondly the kip imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy thirdly the kip allows on one hand to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and on the other hand suggests how we can introduce naturally new distributions finally as a working example of the approach to the non linear kinetics here presented a new non extensive statistics is constructed and studied starting from a one parameter deformation of the exponential function holding the relation f x f x 1

about the modified gaussian family of income distributions with applications to individual incomes abstract in a recent paper in this journal q guo l gao distribution of individual incomes in china between 1992 and 2009 physica a 391 2012 5139 5145 a new family of distributions for modeling individual incomes in china was proposed this family is the so called modified gaussian mg distribution which depends on two parameters the mg distribution shows a satisfactory fit for the individual income data between 1992 and 2009 however for the practical use of this model with individual incomes it is necessary to know its probabilistic and statistical properties especially the corresponding inequality measures in this paper probabilistic functions and inequality measures of the mg distribution are obtained in closed form including the normalizing constant probability functions moments first degree stochastic dominance conditions relationships with other families of distributions and standard tools for inequality measurement lorenz and generalized lorenz curves and gini donaldson weymark kakwani and pietra indices several methods for parameter estimation are also discussed in order to illustrate all the previous formulations we have fitted individual incomes of spain for three years using the european community household panel survey concluding a static pattern of inequality since the gini index and other inequality measures remain constant over the study period

characterization of uninorms on bounded lattices in this paper we propose a characterization of uninorms on a general bounded lattice l by means of a sextuple of a triangular norm a triangular conorm and four aggregation functions on l observe that in the case when l is a chain it is enough to consider a triple consisting of a t norm a t conorm and an averaging aggregation function an example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown note that this cannot happen if we consider uninorms acting on a chain two general constructions of uninorms on l are added letting a t norm a t conorm linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions

distributive and infinitely distributive t norms on complete lattices abstract a relation between the direct decomposability of an infinitely distributive t norm on a complete lattice l and direct decompositions of the neutral element 1 of l is obtained some useful applications of this relation are given in particularly the description of all t 1 lattices without infinitely distributive t norms on complete lattices and the description of all distributive t norms on lattices of length 2 are given the paper also contains the solutions of two open problems

explicit expressions of the pietra index for the generalized function for the size distribution of income abstract the importance of the pietra index in socioeconomic systems and econophysics has been highlighted by eliazar and sokolov 2010 in this paper we obtain closed expressions for the pietra index for the generalized function for the size of income proposed by mcdonald 1984 this family is composed of three classes of distributions the generalized gamma distribution gg the generalized beta of the first kind gb1 and the generalized beta of the second kind gb2 for the different distributions we obtain closed and simple expressions of the pietra index which can be easily computed we also obtain the pietra index for other relevant income models including finite mixtures of distributions and the generalized distribution clementi et al 2008 finally two empirical applications with real income data are given

pseudo t norms and implication operators direct products and direct product decompositions in this paper we further study the pseudo t norms and implication operators on a complete brouwerian lattice and discuss their direct products and direct product decompositions

a new pareto type distribution with applications in reliability and income data a new pareto type distribution is introduced and studied this new model is a generalization of the well known pareto distribution we derive some of its probabilistic and inferential properties we deduce the mathematical form of the lorenz curve and the gini index associated with the new model the maximum likelihood estimators are derived and their performance are evaluated through a monte carlo simulation study finally we illustrate the flexibility of the new distribution by means of three applications to real data sets

on the direct decomposability of t norms on product lattices in this paper a method is presented for constructing t norms on product lattices in other words commutative partially ordered integral monoids over product lattices which are not direct products the method is fairly general and allows to generate a broad class of such t norms this solves an open problem posed in 1999 by de baets and mesiar

pairwise comaximal elements and the classification of all ν distributive triangular norms of length 3 for a lattice with a distributive t norm one useful inequality is obtained theorems on relations between a family of pairwise comaximal elements and a direct decomposition of the unit in a lattice with a distributive t norm have given using these results the description of all distributive triangular norms of length 3 and all lattices of length 3 with a distributive t norm have obtained

nullnorms on bounded lattices nullnorms are generalization of triangular norms and triangular conorms with a zero element in the interior of the unit interval in this paper we generalize nullnorms to an arbitrary bounded lattices we show the existence of nullnorms with zero element a for arbitrary element a l 0 1 using the fact that some t norms and t conorms on an arbitrary fixed bounded lattice l always exist as a by product we give a method of constructing nullnorms using this method we obtain also the smallest nullnorm and the greatest nullnorm with given zero element a some other construction methods for nullnorms are also added

quadratic perturbations of quadratic codimension four centers abstract we study the stratum in the set of all quadratic differential systems x p 2 x y y q 2 x y with a center known as the codimension four case q 4 it has a center and a node and a rational first integral the limit cycles under small quadratic perturbations in the system are determined by the zeros of the first poincare pontryagin melnikov integral i we show that the orbits of the unperturbed system are elliptic curves and i is a complete elliptic integral then using picard fuchs equations and the petrov s method based on the argument principle we set an upper bound of eight for the number of limit cycles produced from the period annulus around the center