analysis of turbulence by statistics based on generalized entropies an analytical formula of the scaling exponents of velocity structure function for fully developed turbulence is derived non perturbatively by assuming that its underlying statistics is the one based on the generalized measures of entropy the renyi entropy or the havrda charvat tsallis hct entropy it is revealed by a self consistent analysis for the observed value 0 220 1 that the formula explains experimental data very well with single value q 0 343 of the index which appears in the measures of the renyi entropy or of the hct entropy the probability density functions of the velocity fluctuation and of the velocity gradient are also presented

power law sensitivity to initial conditions for abelian directed self organized critical models abstract the power law sensitivity to initial conditions is investigated for self organized critical soc models within the damage spreading framework a class of two dimensional abelian directed models are analyzed results for the time evolution of the normalized squared euclidian distance indicate that the propagation of a small perturbation damage has the same behavior even assuming different parameters of these models the same technique applied to a non abelian complete toppling version of a directed model leads to a completely different behavior results also suggest that there might exist a connection between the multifractal spectra of a potential energy measure and the power law sensitivity to initial conditions for the abelian soc models as observed for low dimensional systems

deformations of current lie algebras i small algebras in characteristic 2 abstract we compute low degree cohomology of current lie algebras extended over the 3 dimensional simple algebra compute deformations of related semisimple lie algebras and apply these results to classification of simple lie algebras of absolute toral rank 2 and having a cartan subalgebra of toral rank one everything is in characteristic 2

deformations of w1 n a and modular semisimple lie algebras with a solvable maximal subalgebra abstract in one of his last papers boris weisfeiler proved that if modular semisimple lie algebra possesses a solvable maximal subalgebra which defines in it a long filtration then associated graded algebra is isomorphic to one constructed from the zassenhaus algebra tensored with the divided powers algebra we completely determine such class of algebras calculating in process low dimensional cohomology groups of zassenhaus algebra tensored with any associative commutative algebra

two dimensional dissipative maps at chaos threshold sensitivity to initial conditions and relaxation dynamics abstract the sensitivity to initial conditions and relaxation dynamics of two dimensional maps are analyzed at the edge of chaos along the lines of nonextensive statistical mechanics we verify the dual nature of the entropic index for the henon map one q sen q rel w 1 related to its relaxation dynamics towards its stationary state attractor we also corroborate a scaling law between these two indices previously found for z logistic maps finally we perform a preliminary analysis of a linearized version of the henon map the smoothed lozi map we find that the sensitivity properties of all these z logistic henon and lozi maps are the same q sen 0 2445

general thermostatistical formalisms invariance under uniform spectrum translations and tsallis q additivity the recent proposal by tsallis of a generalized thermostatistics devised to treat systems endowed with long range interactions long range memory eects or a fractal like relevant phase space has raised interesting and profound issues concerning the properties of general thermostatistical formalisms in the present paper we identify families of thermostatistical formalisms that share some fundamental characteristics the canonical ensemble s invariance under uniform translations of the hamiltonian s energy spectrum is shown to be a universal property veried by any thermostatistical formalism based upon linear mean energy constraints we also provide multiparametric families of entropies exhibiting tsallis q additivity law c 1999 elsevier science b v all rights reserved

tsallis statistics and fully developed turbulence an analysis of fully developed turbulence is developed based on the assumption that the underlying statistics of the system is that of the tsallis ensemble the multifractal spectrum ft corresponding to the tsallis type distribution function is determined self consistently in the sense that all parameters can be obtained through the observed value of the intermittency exponent it is shown that the scaling exponents m of the velocity structure function derived with the help of the multifractal spectrum fit very well with experimental data it is revealed that the asymptotic expression of m for m 1 has a log term the present self consistent approach narrowed down the value of intermittency exponent for the fully developed turbulence to 0 235 0 015

structure of basic lie superalgebras and of their affine extensions we generalize to the case of superalgebras several properties of simple lie algebras involving the use of dynkin diagrams if to a simple lie algebra can be associated one dynkin diagram it is a finite set of nonequivalent ones which can be constructed for a basic superalgebra or b s a the knowledge of these diagrams which can be obtained for each b s a in a systematic way allows us to deduce the regular subsuperalgebras of a b s a the symmetries of the dynkin diagrams are related to outer automorphisms of b s a and lead to some singular subsuperalgebras finally we consider the extended dynkin diagrams in order to classify the affine b s a and use their symmetries to construct the twisted basic superalgebras

simple lie algebras of small characteristic ii exceptional roots abstract letlbe a finite dimensional simple lie algebra of absolute toral rank 2 over an algebraically closed field of characteristicp 3 andta 2 dimensional torus in the semisimplep envelope ofl suppose thatlis not isomorphic to a melikian algebra it is proved in this paper that for every root l t the subalgebrak generated by i f pki whereki x li x l i 0 acts triangulably onl in particular this implies that in the terminology of r e block and r l wilson 1988 j algebra114 115 259 all roots of l t are nonexceptional

the jordan structure of lie and kac moody algebras the authors establish a precise relation between the structures of lie and jordan algebras by presenting a method of constructing one type of algebra from the other the examples of the lie algebras associated to simple jordan algebras mm n and clifford algebras are discussed in detail the generalization of such arguments to infinite dimensional lie algebras in terms of fermi fields is also discussed

simple lie algebras of small characteristic iv solvable and classical roots abstract let l be a finite dimensional simple lie algebra over an algebraically closed field f of characteristic p 3 and t a torus of maximal dimension in the p envelope of l in der l in this paper we describe the t semisimple quotients of the 2 sections of l relative to t and prove that if all 1 sections of l relative to t are compositionally classical or solvable then l is either classical or a block algebra or a filtered lie algebra of type s

symmetric function products and plethysms and the boson fermion correspondence we use the boson fermion correspondence for s and q functions to establish some interesting properties concerning outer products and plethysms of s functions or q functions by power sum symmetric functions the techniques which are developed are also applied to computing the inverse kostka foulkes matrix which is the transition matrix between hall littlewood symmetric functions and s functions in some simple cases

tsallis entropy maximization procedure revisited abstract the proper way of averaging is an important question with regards to tsallis thermostatistics three different procedures have been thus far employed in the pertinent literature the third one i e the tsallis mendes plastino tmp physica a 261 1998 534 normalization procedure exhibits clear advantages with respect to earlier ones in this work we advance a distinct from the tmp one way of handling the lagrange multipliers involved in the extremization process that leads to tsallis statistical operator it is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the tsallis mendes plastino formalism

maximum entropy versus minimum risk and applications to some classical discrete distributions the game which can be taken to lie behind the maximum entropy principle is studied refining previous techniques new theoretical results are obtained these results are illustrated by concrete examples pertaining to well known classical models

entanglement and localization transitions in eigenstates of interacting chaotic systems the entanglement and localization in eigenstates of strongly chaotic subsystems are studied as a function of their interaction strength excellent measures for this purpose are the von neumann entropy havrda charv at tsallis entropies and the averaged inverse participation ratio all the entropies are shown to follow a remarkably simple exponential form which describes a universal and rapid transition to nearly maximal entanglement for increasing interaction strength an unexpectedly exact relationship between the subsystem averaged inverse participation ratio and purity is derived that prescribes the transition in the localization as well

path integral approach to the wigner kirkwood expansion we study the high temperature behavior of quantum mechanical path integrals starting from the feynman kac formula we derive a functional representation of the wigner kirkwood perturbation expansion for quantum boltzmann densities as shown by its applications to different potentials the presented expansion turns out to be quite efficient in generating analytic form of the higher order expansion coefficients to put some flesh on the bare bones we apply the expansion to obtain basic thermodynamic functions of the one dimensional anharmonic oscillator further salient issues such as generalization to the bloch density matrix and comparison with the more customary world line formulation are discussed

superalgebras symplectic bosons and the sugawara construction new representations of affine lie algebras are constructed using symplectic bosons of the sort that occur naturally in the brst treatment of fermionic string theories these representations are shown to have analogous properties to the current algebra representations in terms of free fermion fields though they do not act in a positive space in particular the condition for the sugawara construction of the virasoro algebra to equal the free one is the existence of a superalgebra with a quadratic casimir operator paralleling the symmetric space theorem for fermionic field constructions both results are seen to be particular cases of a more general super symmetric space theorem which arises from considering an affinisation of the superalgebras these algebras are realised in terms of free fermions and symplectic bosons and lead to a super sugawara construction of the virasoro algebra the conditions for this to equal a virasoro algebra obtained from the free fields are provided by the super symmetric space theorem

on maximum entropy principle superstatistics power law distribution and renyi parameter abstract the equilibrium distributions of probabilities are derived on the basis of the maximum entropy principle mep for the renyi and tsallis entropies new s forms for the renyi and tsallis distribution functions are found which are normalised with corresponding entropies in contrast to the usual z forms normalised with partition functions z the superstatistics based on the gibbs distribution of energy fluctuations gives rise to a distribution function of the same structure that the renyi and tsallis distributions have the long range tail of the renyi distribution is the power law distribution with the exponent s expressed in terms of the free renyi parameter q as s 1 1 q the condition s 0 gives rise to the requirement q q can be uniquely determined with the use of a further extension of mep as the condition for maximum of the difference between the renyi and boltzmann entropies for the same power law distribution dependent on q it is found that the maximum is realized for q within the range from 0 25 to 0 5 and the exponent s varies from 1 3 to 2 in dependence on parameters of stochastic systems

a modular analogue of morozov s theorem on maximal subalgebras of simple lie algebras abstract let g be a simple algebraic group over an algebraically closed field of characteristic p 0 and suppose that p is a very good prime for g in this paper we prove that any maximal lie subalgebra m of g lie g with rad m 0 has the form m lie p for some maximal parabolic subgroup p of g this means that morozov s theorem on maximal subalgebras is valid under mild assumptions on g we show that such assumptions are necessary by providing a counterexample to morozov s theorem for groups of type e 8 over fields of characteristic 5 our proof relies on the main results and methods of the classification theory of finite dimensional simple lie algebras over fields of prime characteristic

perturbation expansion for option pricing with stochastic volatility abstract we fit the volatility fluctuations of the s p 500 index well by a chi distribution and the distribution of log returns by a corresponding superposition of gaussian distributions the fourier transform of this is remarkably of the tsallis type an option pricing formula is derived from the same superposition of black scholes expressions an explicit analytic formula is deduced from a perturbation expansion around a black scholes formula with the mean volatility the expansion has two parts the first takes into account the non gaussian character of the stock fluctuations and is organized by powers of the excess kurtosis the second is contract based and is organized by the moments of moneyness of the option with this expansion we show that for the dow jones euro stoxx 50 option data a hedging strategy is close to being optimal

simple lie algebras of small characteristic iii the toral rank 2 case abstract it is proved that every finite dimensional simple lie algebra of absolute toral rank 2 over an algebraically closed field of characteristic p 3 is of classical or cartan type or a melikian algebra

vertex operator representations of basic affine superalgebras using the basic construction of the affine superalgebra osp m n 1 in terms of vertex operators vertex operator representations of a large class of untwisted and twisted affine basic superalgebras of the unitary and orthosymplectic series are found the construction uses two methods first the regular embeddings of semisimple superalgebras untwisted case and second the folding method developed in a previous paper frappat et al nucl phys b 305 164 1988 to construct twisted vertex operators for lie algebras with fermionic elementary fields twisted case

maximum entropy principle in statistical inference case for non shannonian entropies in this letter we show that the shore johnson axioms for the maximum entropy principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought apart from a formal side of the proof where a one parameter class of admissible entropies is identified we substantiate our point by analyzing the effect of weak correlations and by discussing two pertinent examples two qubit quantum system and transverse momentum behavior of hadrons in high energy proton proton collisions

simulated annealing with tsallis weights a numerical comparison abstract we discuss the use of tsallis generalized mechanics in simulated annealing algorithms for a small peptide it is shown that older implementations are not more effective than regular simulated annealing in finding ground state configurations we propose a new implementation which leads to an improvement over regular simulated annealing

on q non extensive statistics with non tsallisian entropy we combine an axiomatics of renyi with the qq deformed version of khinchin axioms to obtain a measure of information i e entropy which accounts both for systems with embedded self similarity and non extensivity we show that the entropy thus obtained is uniquely solved in terms of a one parameter family of information measures the ensuing maximal entropy distribution is phrased in terms of a special function known as the lambert w function we analyze the corresponding high and low temperature asymptotics and reveal a non trivial structure of the parameter space salient issues such as concavity and schur concavity of the new entropy are also discussed

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

on the structure of the graded lie algebra associated with a noncontractible filtration the largest r 0 such that g 0 is called the depth of g any such yr g is semisimple and contains a unique minimal homogeneous ideal which will be denoted as g9 the structure of g9 can be described in terms of derivation simple commutative associative graded algebras and simple w x graded lie algebras 23 there are two cases nondegenerate and degenerate in the terminology of weisfeiler which expose different features these two are distinguished by whether g9 has a nonzero positive part or

some finite varieties of lie algebras in the class whenever all n generated subalgebras of l are in the class thus the classes jv of nilpotent lie algebras and d of abelian lie algebras are 2 recognizable the problems are to find if a given class is n recognizable and to find the smallest n we consider the classes jv of lie algebras which have an abelian ideal with nilpotent quotient jv of lie algebras which have a nilpotent ideal with abelian quotient of supersolvable lie algebras and y of solvable lie algebras the same notation is used for the corresponding classes of finite groups most notation is standard except where indicated

infinite chiral symmetry in four dimensions we describe a new correspondence between four dimensional conformal field theories with extended supersymmetry and two dimensional chiral algebras the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four dimensional theory infinite chiral symmetry has far reaching consequences for the spectral data correlation functions and central charges of any four dimensional theory with mathcal n 2 superconformal symmetry

maximal subalgebras of simple modular lie algebras abstract the maximal graded subalgebras of the restricted simple lie algebras of cartan type w n s n h n and k n are studied the notion of an r subalgebra and that of an s subalgebra are introduced for maximal subalgebras all maximal r subalgebras are described completely the number of conjugacy classes representatives of conjugacy classes and the dimensions of all r subalgebras are found an invariant description of graded s subalgebras is also obtained

tsallis thermostatics as a statistical physics of random chains in this paper we point out that the generalized statistics of tsallis havrda charvat can be conveniently used as a conceptual framework for statistical treatment of random chains in particular we use the path integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented random loop of arbitrary length and shape in a background scalar potential to put some meat on the bare bones we illustrate this with two statistical systems schultz zimm polymer and relativistic particle further salient issues such as the projective special linear group psl 2 r transformation properties of tsallis inverse temperature parameter and a grand canonical ensemble of fluctuating random loops related to the tsallis havrda charvat statistics are also briefly discussed

classification of the restricted simple lie algebras soit l une algebre de lie simple restreinte de dimension finie sur un corps algebriquement clos f de caracteristique p 7 alors l est de type classique ou de cartan

tori in the melikian algebra this paper is concerned with the tori in the restricted melikian algebra g g 1 1 according to the latest classification result of premet and strade 16 g is the unique simple lie algebra of toral rank 2 over an algebraically closed field of characteristic p 5 distinct from the classical algebras and algebras of cartan type here we determine the one dimensional subtori in g up to conjugation by automorphisms and compute their centralizers in g one consequence of this investigation is that all maximal tori in g are two dimensional for each two dimensional torus we find the number of its roots of any possible type classical witt hamiltonian proper the answer depends only on the position of the torus relative to the invariant filtration of g the conjugacy classes of two dimensional tori are not determined in this paper it can be shown that their number is infinite the classification of simple lie algebras requires detailed information about the toral structure of low rank lie algebras see e g 3 19 one of the key points is the possibility of finding a torus of maximal dimension in the p envelope of a simple lie algebra l having all roots proper the classical argument is based on checking that when switching an improper root to a proper one the number of proper roots in every 2 section of l increases in the case of the melikian algebra we encounter a situation when the number of proper roots remains unchanged when this does occur we show that the number of hamiltonian roots becomes strictly less

local time representation of path integrals we derive a local time path integral representation for a generic one dimensional time independent system in particular we show how to rephrase the matrix elements of the bloch density matrix as a path integral over x dependent local time profiles the latter quantify the time that the sample paths x t in the feynman path integral spend in the vicinity of an arbitrary point x generalization of the local time representation that includes arbitrary functionals of the local time is also provided we argue that the results obtained represent a powerful alternative to the traditional feynman kac formula particularly in the high and low temperature regimes to illustrate this point we apply our local time representation to analyze the asymptotic behavior of the bloch density matrix at low temperatures further salient issues such as connections with the sturm liouville theory and the rayleigh ritz variational principle are also discussed

on simple lie algebras over a field of characteristic 2 abstract we prove that the simple lie algebras constructed by g jurman 2004 in 2 are isomorphic to hamiltonian algebras as a corollary we answer all questions formulated in g jurman 2004 2 about isomorphisms of these algebras

superpositions of probability distributions probability distributions which can be obtained from superpositions of gaussian distributions of different variances v ensuremath sigma 2 play a favored role in quantum theory and financial markets such superpositions need not necessarily obey the chapman kolmogorov semigroup relation for markovian processes because they may introduce memory effects we derive the general form of the smearing distributions in v which do not destroy the semigroup property the smearing technique has two immediate applications it permits simplifying the system of kramers moyal equations for smeared and unsmeared conditional probabilities and can be conveniently implemented in the path integral calculus in many cases the superposition of path integrals can be evaluated much easier than the initial path integral three simple examples are presented and it is shown how the technique is extended to quantum mechanics

toral rank one lie algebras let l be a finite dimensional lie algebra over an algebraically closed field f of characteristic p 0 assume that h is a cartan subalgebra of l we say that l has toral rank m relative to h if dim pa m where a is the set of roots with respect to h p is the prime field and pa is the p vector space spanned by a in this work we study lie algebras of toral rank one the motivation to investigate this class of algebras comes from the problem of classifying simple lie algebras if a is a finite dimensional simple lie algebra with cartan subalgebra h and if ci is a root of h then the subalgebra a ciep a has toral rank one relative to h in 12 133 wilson has shown that if a simple algebra a has characteristic p 7 then the restricted closure w of h in der a has the form r t z where i is the nil radical of b and t is the maximal torus which is central in j it follows that ad r on each root space a can be simultaneously upper triangularized indeed i is a lie algebra of nilpotent transformations on a and thus by 8 theorem 3 31 it annihilates a nonzero vector the space of such vectors is t invariant and so t i has a common eigenvector u on a one can proceed inductively on ajfu to argue that each root space a has a basis relative to which ad r is upper triangular with that in mind we say in what follows that a cartan subalgebra his triangularizable if there is a basis for each root space relative to which ad h is upper triangular we show in section 1 that if l is a lie algebra having a toral rank one cartan subalgebra h and if h is triangularizable then l modulo its maximal solvable ideal either is 0 or consists of a simple toral rank one lie algebra s together with derivations of s in h in the first case we say that the core of l is 0 and in the second case that the core of l is s wilson 141 has classified the simple toral rank one lie algebras using

c sections of lie algebras let m be a maximal subalgebra of a lie algebra l and a b a chief factor of l such that b m and a 6 m we call the factor algebra m a b a c section of m all such c sections are isomorphic and this concept is related those of c ideals and ideal index previously introduced by the author properties of c sections are studied and some new characterizations of solvable lie algebras are obtained mathematics subject classification 2000 17b05 17b20 17b30 17b50

the classification of the simple modular lie algebras ii the toral structure abstract let l be a simple lie algebra over an algebraically closed field of characteristic p 7 and t an optimal torus in some p envelope l p we determine the action of t on the two sections of l which have been described in st4 we also give some new and noncomputational proofs to determine the conjugacy classes of the tori in w n 1 and of the cartan subalgebras of w 1 n

a note on bounded entropies abstract the aim of the paper is to study the link between non additivity of some entropies and their boundedness we propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual additive group this allows to show that the entropies that are additive with respect to the addition of the group for independent random variables are nonlinear transforms of the renyi entropies including the particular case of the shannon entropy as a particular example we study as a group a bounded interval in which the addition is a generalization of the addition of velocities in special relativity we show that tsallis havrda charvat entropy is included in the family of entropies we define finally a link is made between the approach developed in the paper and the theory of deformed logarithms

analysis of tsallis classical partition function s poles abstract when one integrates the q exponential function of tsallis so as to get the partition function z a gamma function inevitably emerges consequently poles arise we investigate here the thermodynamic significance of these poles in the case of n classical harmonic oscillators ho given that this is an exceedingly well known system any new feature that may arise can safely be attributed to the poles effect we appeal to the mathematical tools used in plastino et al 2016 and plastino and rocca 2017 and obtain both bound and unbound states in the first case we are then faced with a classical einstein crystal we also detect what might be interpreted as pseudo gravitational effects

simple lie algebras of characteristic p with dependent roots we investigate finite dimensional simple lie algebras over an algebraically closed field f of characteristic p 7 having a cartan subalgebra h whose roots are dependent over f we show that h must be one dimensional or for some root a relative to h there is a 1 section l a such that the core of l a is a simple lie algebra of cartan type h 2 mr d 2 or w 1 n for some n 1 the results we obtain have applications to studying the local behavior of simple lie algebras and to classifying simple lie algebras which have a cartan subalgebra of dimension less than p 2

pdf of velocity fluctuation in turbulence by a statistics based on generalized entropy an analytical formula for the probability density function pdf of the velocity fluctuation in fully developed turbulence is derived non perturbatively by assuming that its underlying statistics is the one based on the generalized measures of entropy the renyi entropy or the tsallis entropy the parameters appearing in the pdf including the index q in the generalized measures are determined self consistently with the help of the observed value of the intermittency exponent the derived pdf explains quite well the experimentally observed density functions

on statistical properties of jizba arimitsu hybrid entropy abstract jizba arimitsu entropy also called hybrid entropy combines axiomatics of renyi and tsallis entropy it has many common properties with them on the other hand some aspects as e g maxent distributions are different in this paper we discuss statistical properties of hybrid entropy we define hybrid entropy for continuous distributions and its relation to discrete entropy additionally definition of hybrid divergence and its connection to fisher metric is also presented interestingly fisher metric connected to hybrid entropy differs from corresponding fisher metrics of renyi and tsallis entropy this motivates us to introduce average hybrid entropy which can be understood as an average between tsallis and renyi entropy

rescuing the maxent treatment for q generalized entropies abstract it has been recently argued that the maxent variational problem would not adequately work for renyi s and tsallis entropies we constructively show here that this is not so if one formulates the associated variational problem in a more orthodox functional fashion

vertex operator construction of nonassociative algebras and their affinizations a general method for the vertex operator construction of nonassociative algebras and triple systems and their super analogs is given using this method the natural affine extensions of these algebraic structures can be defined and constructed essentially all the algebraic structures of physical theories based on point particles can be constructed this way conversely these methods can be used to define the stringy analogs of these algebraic structures

option pricing beyond black scholes based on double fractional diffusion abstract we show how the prices of options can be determined with the help of double fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the black scholes formula

the classification of the simple modular lie algebras iii solution of the classical case we investigate the structure of simple modular lie algebras over an algebraically closed field of characteristic p 7 if the distinguished subalgebra q l t with respect to an optimal torus t in some p envelope lp of l equals l then either l has a two section of type h 2 1 z or l is of classical type