nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

on the membership of hankel operators in a class of lorentz ideals abstract recall that the lorentz ideal c p is the collection of operators a satisfying the condition a p j 1 j p 1 p s j a consider hankel operators h f h 2 s l 2 s d h 2 s where h 2 s is the hardy space on the unit sphere s in c n in this paper we characterize the membership h f c p 2 n p

on uniqueness theorems for tsallis entropy and tsallis relative entropy the uniqueness theorem for tsallis entropy was presented in h suyari ieee trans inf theory vol 50 pp 1783 1787 aug 2004 by introducing the generalized shannon khinchin axiom in the present correspondence this result is generalized and simplified as follows generalization the uniqueness theorem for tsallis relative entropy is shown by means of the generalized hobson s axiom simplification the uniqueness theorem for tsallis entropy is shown by means of the generalized faddeev s axiom

nonextensive entropies derived from form invariance of pseudoadditivity the form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies nonextensive entropy is defined as the appropriate expectation value of nonextensive information content similar to the definition of shannon entropy information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity the satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies the proposed principle requires the same normalization as that derived previously a k rajagopal and s abe phys rev lett 83 1711 1999 but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems

information theory based on nonadditive information content we generalize shannon s information theory in a nonadditive way by focusing on the source coding theorem the nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy some general properties of the nonadditive information entropy are studied in addition the relation between the nonadditivity q and the codeword length is pointed out

an efficient computation scheme for the free space green s function of a two dimensional semiinfinite phased array a simple scheme is developed to compute the green s function of a periodic semiinfinite array in free space it is based on the spectral representation of the fields radiated by an infinite linear array of dipoles results related to successive linear arrays are added in the space domain this summation can be accelerated tremendously by using an elementary extrapolation technique the resulting formulation converges everywhere in the plane containing the array and the number of terms required to achieve a given precision increases slowly away from this plane

on the essential commutant of the toeplitz algebra on the bergman space let tt be the c c algebra generated by the toeplitz operators tf f l b dv tf f l b dv on the bergman space of the unit ball we show that the essential commutant of tt equals tg g vobdd k tg g vobdd k where vobddvobdd is the collection of bounded functions of vanishing oscillation on b and kk denotes the collection of compact operators on la2 b dv

an axiomatic characterization of a two parameter extended relative entropy the uniqueness theorem for a two parameter extended relative entropy is proven this result extends our previous one the uniqueness theorem for a one parameter extended relative entropy to a two parameter case in addition the properties of a two parameter extended relative entropy are studied

characterizations of certain classes of hankel operators on the bergman spaces of the unit disk let f be an integrable function on the unit disk the hankel operator hf is densely defined on the bergman space ap by hfg fg p fg where g is a bounded analytic function and p is the bergman projection orthogonal projection from l2 to a2 extended to l1 via its integral formula in this paper the functions f for which hf extends to a bounded operator from ap to lp are characterized 1 p also characterized are the functions f for which hf extends to a compact or schatten class operator on a2 the proofs can be extended to handle any smoothly bounded domain in c in place of the unit disk

bmo in the bergman metric on bounded symmetric domains for bounded symmetric domains in cn a notion of bounded mean oscillation in terms of the bergman metric is introduced it is shown that for in l2 dv is in bmo if and only if the densely defined operator m p m p pm on l2 dv is bounded here m is multiplication by and p is the bergman projection with range the bergman subspace h2 dv la2 dv of holomorphic functions in l2 dv an analogous characterization of compactness for m p is provided by functions of vanishing mean oscillation at the boundary of

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

new features of quantum discord uncovered by q entropies the notion of quantum discord introduced by ollivier and zurek phys rev lett 88 2001 017901 see also henderson and vedral j phys a 34 2001 6899 has attracted increasing attention in recent years as an entropic quantifier of non classical features pertaining to the correlations exhibited by bipartite quantum systems here we generalize the notion so as to encompass power law q entropies that reduce to the standard shannon entropy in the limit q 1 and study the concomitant consequences the ensuing new discord like measures we advance describe aspects of non classicality that are different from those associated with the standard quantum discord a particular manifestation of this difference concerns a feature related to order let d1 stand for the standard shannon based discord measure and dq for the q 1 one if two quantum states a b are such that d1 a d1 b this order relation does not remain invariant under a change from d1 to dq

on the maximum entropy principle and the minimization of the fisher information in tsallis statistics we give a new proof of the theorems on the maximum entropy principle in tsallis statistics that is we show that the q canonical distribution attains the maximum value of the tsallis entropy subject to the constraint on the q expectation value and the q gaussian distribution attains the maximum value of the tsallis entropy subject to the constraint on the q variance as applications of the non negativity of the tsallis relative entropy without using the lagrange multipliers method in addition we define a q fisher information and then prove a q cramer rao inequality that the q gaussian distribution with special q variances attains the minimum value of the q fisher information

schatten class membership of hankel operators on the unit sphere abstract let h 2 s be the hardy space on the unit sphere s in c n n 2 consider the hankel operator h f 1 p m f h 2 s where the symbol function f is allowed to be arbitrary in l 2 s d we show that for p 2 n h f is in the schatten class c p if and only if f p f belongs to the besov space b p to be more precise the if part of this statement is easy the main result of the paper is the only if part we also show that the membership h f c 2 n implies f p f 0 i e h f 0

generalization of shannon khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy tsallis entropy one parameter generalization of shannon entropy has been often discussed in statistical physics as a new information measure this new information measure has provided many satisfactory physical interpretations in nonextensive systems exhibiting chaos or fractal we present the generalized shannon khinchin axioms to nonextensive systems and prove the uniqueness theorem rigorously our results show that tsallis entropy is the simplest among all nonextensive entropies by the detailed comparisons of our axioms with the previously presented two sets of axioms we reveal the peculiarity of pseudoadditivity as an axiom in this correspondence the most fundamental basis for tsallis entropy as information measure is established in the information theoretic framework

bergman commutators and norm ideals let p be the orthogonal projection from l2 b dv onto the bergman space la2 b dv of the unit ball in cn in this paper we characterize the membership of commutators of the form mf p in the norm ideal c where the symmetric gauge function is allowed to be arbitrary

generalized statistics framework for rate distortion theory abstract variational principles for the rate distortion rd theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of tsallis for values of the nonextensivity parameter satisfying 0 q 1 and q 1 alternating minimization numerical schemes to evaluate the nonextensive rd function are derived numerical simulations demonstrate the efficacy of generalized statistics rd models

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

comment on note on generalization of shannon theorem and inequality kwork sau fa 1998 j phys a math gen 31 8159 has shown an inequality s ab s a s b 1 q s a s b for two interacting systems a and b a typical example of s a is the tsallis entropy as stated in his paper however there exist many counterexamples to the above inequality the reason leading to the incorrect result is also presented

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

fundamental properties of tsallis relative entropy fundamental properties for the tsallis relative entropy in both classical and quantum systems are studied as one of our main results we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by hiai and petz the monotonicity of the quantum tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible the generalized tsallis relative entropy is defined and its subadditivity is shown by its joint convexity moreover the generalized peierls bogoliubov inequality is also proven

commutators and localization on the drury arveson space let f be a multiplier for the drury arveson space hn2 of the unit ball and let 1 n denote the coordinate functions we show that for each 1 i n the commutator mf m i belongs to the schatten class cp p 2n this leads to a localization result for multipliers

asymptotically scale invariant occupancy of phase space makes the entropy sq extensive phase space can be constructed for n equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated if they are locally correlated we expect the boltzmann gibbs entropy s bg k i p i ln p i to be extensive i e s bg n n for n in particular if they are independent s bg is strictly additive i e s bg n ns bg 1 n however if the subsystems are globally correlated we expect for a vast class of systems the entropy s q k 1 i p q i q 1 with s 1 s bg for some special value of q 1 to be the one which is extensive i e s q n n for n another concept which is relevant is strict or asymptotic scale freedom or scale invariance defined as the situation for which all marginal probabilities of the n system coincide or asymptotically approach for n the joint probabilities of the n 1 system if each subsystem is a binary one scale freedom is guaranteed by what we hereafter refer to as the leibnitz rule i e the sum of two successive joint probabilities of the n system coincides or asymptotically approaches the corresponding joint probability of the n 1 system the kinds of interplay of these various concepts are illustrated in several examples one of them justifies the title of this paper we conjecture that these mechanisms are deeply related to the very frequent emergence in natural and artificial complex systems of scale free structures and to their connections with nonextensive statistical mechanics summarizing we have shown that for asymptotically scale invariant systems it is s q with q 1 and not s bg the entropy which matches standard clausius like prescriptions of classical thermodynamics

scattering from finite by infinite arrays of slots in a thin conducting wedge the radar scattering from a finite by infinite array of slots cut into a thin conducting wedge is considered the wedge is formed by taking a thin ground plane and applying a bend to create a sharp edge which is parallel to the columns of slots in the infinite axis results are derived for thin linear slots whose major axes are either parallel or perpendicular to the edge a hybrid moment method and geometrical theory of diffraction approach is used with magnetic current expansion functions defined using floquet s theorem on single columns of slots predictions generally agree with scattering measurements of finite by finite array physical models with monostatic patterns taken in a plane orthogonal to the sharp edge

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

note on generalization of shannon theorem and inequality recently santos obtained a generalized entropy using four assumptions which stated that an entropy must i be a continuous function of the probabilities ii be a monotonic increasing function of the number of states w in the case of equiprobability iii satisfy where a and b are two independent systems and iv satisfy the relation where and santos showed that the only function which satisfies all of these properties is the generalized tsallis entropy in this paper we perform a similar analysis and we obtain a family of entropies which are equivalent to the tsallis entropy we also discuss the shannon inequality in the context of the generalized tsallis entropy

generalization of shannon s theorem for tsallis entropy by using the assumptions that the entropy must i be a continuous function of the probabilities pi pi 0 1 i only ii be a monotonic increasing function of the number of states w in the case of equiprobability iii satisfy the pseudoadditivity relation sq a b k sq a k sq b k 1 q sq a sq b k2 a and b being two independent systems q r and k a positive constant and iv satisfy the relation sq pi sq pl pm pl qsq pi pl pm qsq pi pm where pl pm 1 pl i 1wlpi and pm i wl 1wpi we prove along shannon s lines that the unique function that satisfies all these properties is the generalized tsallis entropy sq k 1 i 1wpiq q 1

numerical analysis of finite frequency selective surfaces with rectangular patches of various aspect ratios the finite frequency selective surface studied consists of a two dimensional array finite in one dimension and infinite in the other of perfectly electrically conducting plates in free space the analysis uses a green s function formulation in the spectral domain and the resulting equation is solved using the method of moments techniques are demonstrated for increasing the speed of the numerical computation so that the problem can be solved on a vax 11 780 in a reasonable amount of time two types of basis functions one subsectional and the other complete domain are used to represent the currents on the patches both yield similar results and both are suitable for use in this problem techniques are demonstrated for approximating the tails of the infinite integrations which allow a more accurate solution than truncation results for scattered power density and patch currents illustrate the edge effect and incident angle dependencies results showing 3 db bandwidth resonance peak versus frequency and scattered power versus frequency are plotted for patches with aspect ratios varying from 0 1 to 1

a local inequality for hankel operators on the sphere and its application abstract let h 2 s be the hardy space on the unit sphere s in c n we establish a local inequality for hankel operators h f 1 p m f h 2 s as an application of this local inequality we characterize the membership of h f in the lorentz like ideal c p 2 n p

some general properties of unified entropies basic properties of the unified entropies are examined the consideration is mainly restricted to the finite dimensional quantum case bounds in terms of ensembles of quantum states are given both the continuity in fannes sense and stability in lesche s sense are shown for wide ranges of parameters in particular uniform estimates are obtained for the quantum renyi entropies stability properties in the thermodynamic limit are discussed as well it is shown that the unified entropies enjoy both the subadditivity and triangle inequality for a certain range of parameters non decreasing of all the unified entropies under projective measurements is proved

scaled bregman divergences in a tsallis scenario abstract there exist two different versions of the kullback leibler divergence k ld in tsallis statistics namely the usual generalized k ld and the generalized bregman k ld problems have been encountered in trying to reconcile them a condition for consistency between these two generalized k ld forms is derived by recourse to the additive duality of tsallis statistics it is also shown that the usual generalized k ld subjected to this additive duality known as the dual generalized k ld is a scaled bregman divergence this leads to an interesting conclusion the dual generalized mutual information is a scaled bregman information the utility and implications of these results are discussed

the q gamma and q q polygamma functions of tsallis statistics abstract an axiomatic definition is given for the q gamma function q x q r q 0 x r of tsallis non extensive statistical physics the continuous analogue of the q factorial of suyari h suyari physica a 368 1 2006 63 and the q analogue of the gamma function x of euler and gauss a working definition in closed form based on the hurwitz and riemann zeta functions including their analytic continuations is shown to satisfy this definition several relations involving the q gamma and other functions are obtained the q q polygamma functions q q m x m n defined by successive derivatives of ln q q x where ln q a 1 q 1 a 1 q 1 a 0 is the q logarithmic function are also reported the new functions are used to calculate the inferred probabilities and multipliers for tsallis systems with finite numbers of particles n

information theoretical properties of tsallis entropies a chain rule and a subadditivity for the entropy of type which is one of the nonadditive entropies were derived by daroczy in this paper we study the further relations among tsallis type entropies which are typical nonadditive entropies the chain rule is generalized by showing it for tsallis relative entropy and the nonadditive entropy we show some inequalities related to tsallis entropies especially the strong subadditivity for tsallis type entropies and the subadditivity for the nonadditive entropies the subadditivity and the strong subadditivity naturally lead to define tsallis mutual entropy and tsallis conditional mutual entropy respectively and then we show again chain rules for tsallis mutual entropies we give properties of entropic distances in terms of tsallis entropies finally we show parametrically extended results based on information theory

application of kummer s transformation to the efficient computation of the 3 d green s function with 1 d periodicity the 3 d homogeneous green s function with 1 d periodicity is commonly expressed as spatial and spectral infinite series that may show very slow convergence in this work kummer s transformation is applied to the spatial series in order to accelerate its convergence by retaining a sufficiently large number of asymptotic terms in the application of kummer s transformation the spatial series is split into a set of series which can be accurately obtained with very low computational effort the numerical results obtained show that when the number of asymptotic terms retained in kummer s transformation is large enough the convergence acceleration method proposed in this work is always faster than existing acceleration methods such as the spectral kummer poisson s method and ewald s method