rigorous properties and uncertainty like relationships on product complexity measures application to atomic systems most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework valid for any arbitrary n dimensional distribution in the present work different product complexities constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated different results on product complexities such as rigorous bounds uncertainty like inequalities relationships among themselves and also statistical interpretations are given for the sake of completeness some of these analytical results on product complexities are numerically checked for the one particle densities of atomic systems in both conjugated spaces

on a non linear formulation for curved timoshenko beam elements considering large displacement rotation increments summary an incremental total lagrangian formulation for curved beam elements that includes the effect of large rotation increments is developed a complete and symmetric tangent stiffness matrix is obtained and the numerical results show in general an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix

when shannon and khinchin meet shore and johnson equivalence of information theory and statistical inference axiomatics we propose a unified framework for both shannon khinchin and shore johnson axiomatic systems we do it by rephrasing shannon khinchine axioms in terms of generalized arithmetics of kolmogorov and nagumo we prove that the two axiomatic schemes yield identical classes of entropic functionals the uffink class of entropies this allows to re establish the entropic parallelism between information theory and statistical inference that has seemed to be broken by the use of non shannonian entropies

stock market and motion of a variable mass spring we establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock market dynamics within an economic model based on simple temporal demand and supply functions e canessa j phys a 33 2000 3637 the total system energy et is shown to be proportional to a decreasing time dependent spring constant kt this model allows to derive log periodicity cos log t tc on commodity prices and oscillations surplus and shortages in the level of stocks we also made an attempt to connect these results to the tsallis statistics parameter q based on a possible force entropy correlation e canessa physica a 341 2004 165 and find that the tsallis second entropic term i 1wpiq q 1 relates to the square of the demand or supply function

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

finite rotation quadrilateral element for multi layer beams the paper presents the finite rotations beam equations derived on use of the generalized reissner hypothesis with a scalar parameter for the transverse extension the beam strain and change of curvature measures are obtained from the right stretch strain and the virtual work is given for biot type stress and couple resultants the strain energy for the first order isotropic elastic material is assumed in terms of the right stretch strain and constitutive equations for the beam stress and couple resultants are derived two finite rotation elements are developed from the derived beam equations a beam element with the transverse stretch and a quadrilateral element first the beam element with the uniformly under integrated tangent operator is developed next the formula linking the middle line variables and the interface variables of the beam is introduced consistently with the generalized reissner kinematics linearization of this formula is performed and the derived tangent operator is used to convert the two node beam element to a four node quadrilateral both the finite elements have been tested on several numerical examples some of highly non linear characteristics and their accuracy is very good it has been established that the quadrilateral element which is intended for applications to multi layer beams performs very well for high elemental aspect ratios and can therefore be applied to modelling of very thin layers copyright 1999 john wiley sons ltd

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

generalized shannon khinchin axioms and uniqueness theorem for pseudo additive entropies abstract we consider the shannon khinchin axiomatic systems for the characterization of generalized entropies such as the sharma mittal and frank daffertshofer entropies we provide the generalization of the shannon khinchin axioms and give the corresponding uniqueness theorem the previous attempts at such axiomatizations are also discussed

deformed exponentials and logarithms in generalized thermostatistics abstract criteria are given that deformed logarithmic and exponential functions should satisfy with a pair of such functions one can associate another function called the deduced logarithmic function it is shown that generalized thermostatistics can be formulated in terms of deformed exponential functions together with the associated deduced logarithmic functions

thermodynamics from first principles correlations and nonextensivity the standard formulation of thermostatistics being based on the boltzmann gibbs distribution and logarithmic shannon entropy describes idealized uncorrelated systems with extensive energies and short range interactions in this rapid communication we use the fundamental principles of ergodicity via liouville s theorem the self similarity of correlations and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long range interacting systems significantly our formalism provides a justification for the well studied nonextensive thermostatistics characterized by the tsallis distribution which it includes as a special case we also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the gibbs shannon entropy the consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics

age innovations and time operator of networks abstract we extend the time operator and age to network evolution models internal age formulas and the distribution of innovations are computed for erd s renyi random networks for markov networks and barabasi albert preferential attachment networks the innovation probabilities are found to be proportional to the quadratic entropy which coincides with the tsallis entropy for entropic index q 2 in all markov networks as well as in the linear growth mechanism the distribution of innovations in the barabasi albert model is a new probability distribution of the logarithmic type

implicit multigrid algorithms for incompressible turbulent flows on unstructured grids an implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described the foundation of the code is a backward euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned generalized minimal residual gmres technique for the gmres calculations several techniques are investigated for forming the matrix vector product convergence acceleration is achieved through a multigrid scheme that uses nonnested coarse grids that are generated using a technique described in the present paper convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four element airfoil viscous results which are compared with experimental data include the turbulent flow over a naca 4412 airfoil a three element airfoil for which mach number effects are investigated and three dimensional flow over a wing with a partial span flap

high resolution upwind schemes for the three dimensional incompressible navier stokes equations based on flux difference splitting implicit high resolution schemes are constructed for efficient computations of steady state solution to the three dimensional incompressibl e navier stokes equations in curvilinear coordinates these schemes use first order accurate euler backward time differencing and second order central differencing for the viscous shear fluxes up to third order accurate upwind differencing is achieved through a reconstruction of the solution from its cell averages the reconstruction is accomplished by linear interpolation where the node stencils are selected such that in regions of smooth solution the flow is highly resolved while spurious oscillations in regions of rapid changes in gradient are still suppressed fairly rapid convergence to steady state solutions is attained with a vectorizable hybrid time marching method flows around a sharp edged delta wing are computed with the maximum accuracy of the upwind differencing restricted to first second and third order to illustrate the effect of accuracy oh the global and on the local vortical flowfields the results are validated with experimental data i introduction t here are basically two options to compute threedimensional low speed flows as steady state solutions to the navier stokes equations numerical approximations 1 to the compressible navier stokes equations for low mach numbers m or 2 to the incompressible navier stokes equations in view of the numerous time dependent methods both explicit1 and implicit 2 4 for the compressible navier stokes equations the first option appears to be a viable choice however the efficiency of these schemes deteriorates considerably with decreasing subsonic mach number due to the stiffness of the physical problems associated with lowspeed viscous flow the stiffness arises from both disparate characteristic speeds and length scales furthermore the accuracy of low speed flowfield computations with implicit approximate factorization af schemes e g those in refs 2 4 becomes questionable for low mach numbers since the factorization errors increase in an unbounded fashion for a decreasing mach number 5 that suggests to remove the sound speed time scale and to assume the flow to be truly incompressible aziz and heliums6 proposed to solve the navier stokes equations for incompressible fully three dimensional flow in a vector potential vorticity formulation because of its storage requirements and the necessity to solve three poisson equations at each time level that method failed to become popular that leaves solving the navier stokes equations for threedimensional incompressible flow in their primitive variable formulation common methods for this formulation advance the solution for the velocity field by explicitly or implicitly solving the equations of motion the updated velocity field is used to compute the corresponding pressure field by solving a poisson equation7 or by an iterative procedure with the equation of continuity as a compatibility condition 8 such schemes

a generalized statistical complexity measure applications to quantum systems a two parameter family of complexity measures c based on the renyi entropies is introduced and characterized by a detailed study of its mathematical properties this family is the generalization of a continuous version of the lopez ruiz mancini calbet complexity which is recovered for 1 and 2 these complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system when one of the parameters or goes to infinity one of the global factors becomes a local factor for this special case the complexity is calculated on different quantum systems h atom harmonic oscillator and square well

stability of vortex pairs over slender conical bodies analysis and numerical computation doi 10 2514 1 33498 analytical studies and computational fluid dynamics simulations are presented to study the formation and stability of stationary symmetric and asymmetric vortex pairs over slender conical bodies in an inviscid incompressible flow at high angles of attack the analytical method is based on an eigenvalue analysis on the motion of the vortices under small perturbations a three dimensional time accurate euler code is used to compute five typical flowsstudiedbythe analytical methodon extraordinarily finegrids withstrict convergence criteria both the theory and the computation show that the vortices over a delta wing are stable and those over a wing body configuration at the low angle of attack are symmetric and stable but become asymmetric and bistable at higher angles of attack that is the vortices shift to one of two stable mirror imaged asymmetric configurations the computational results agree well with the analytical predictions demonstrating the existence of a global inviscid hydrodynamic instability mechanism responsible for the asymmetry of separation vortices over slender conical bodies

multigrid acceleration of the flux split euler equations multigrid acceleration is applied to a flux split algorithm for solving the euler equations in three dimensions the basic algorithm is an implicit spatially split approximate factorization method the stability and performance of the scheme in comparison to other factorizations are examined results are presented for three dimensional flows that demonstrate substantially unproved convergence with the multigrid algorithm

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

a new class of entropic information measures formal group theory and information geometry in this work we study generalized entropies and information geometry in a group theoretical framework we explore the conditions that ensure the existence of some natural properties and at the same time of a group theoretical structure for a large class of entropies in addition a method for defining new entropies using previously known ones with some desired group theoretical properties is proposed in the second part of this work the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied finally a method of constructing new divergences from known ones is discussed in particular some results concerning the riemannian structure associated with the class of divergences under investigation are formulated

performance of three dimensional compressible navier stokes codes at low mach numbers the low mach number performance of two widely used three dimensional compressible navier stokes solvers is examined both of the codes employ a finite volume formulation but differ in their respective discretization and solution schemes in the first code a central difference discretization is employed and solutions are obtained using an explicit runge kutta time stepping scheme in the second code an upwind biased discretization is used and an implicit approximate factorization scheme is employed the accuracy and efficiency of the codes are assessed by comparison with results from an incompressible navier stokes solver and experimental data the test cases examined include an untwisted rectangular wing and a wing fuselage configuration the computed pressure distributions were nearly identical and agreed quite well with experimental data in addition the predicted pressure distributions were nearly identical to those predicted by the incompressible flow solver the influence of freestream mach number on the efficiency of both compressible flow solvers also is examined

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

entropy and complexity analysis of dirac delta like quantum potentials abstract the dirac delta like quantum mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics condensed matter and quantum computation the entropy and complexity properties of potentials with one and two dirac delta functions are here analytically calculated and numerically discussed in both position and momentum spaces we have studied the information theoretic lengths of fisher renyi and shannon types as well as the cramer rao fisher shannon and lmc shape complexities of the lowest lying stationary states of one delta and twin delta they allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation

radiated noise from airfoils in realistic mean flows the long term objective of the research described is to use computational aeroacoustics methodology and parallel computers to increase the understanding of broadband blade noise in a systematic progression toward simulations of completely realistic configurations and conditions some simplified problems that address the important features of the flow are investigated a two dimensional navier stokes code implemented using the message passing library and fortran 90 on the ibm sp2 is used to perform the calculations results are presented for the interaction of a vortical gust and naca airfoils including nonlinear effects the influence of gust frequency and airfoil thickness is described a multigrid method is used to obtain converged steady state solutions before the gust is introduced in a source region inside the domain

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

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

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

renyi s information transfer between financial time series a b s t r a c t in this paper we quantify the statistical coherence between financial time series by means of the renyi entropy with the help of campbell s coding theorem we show that the renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others this accentuation is controlled with renyi s parameter q to tackle the issue of the information flow between time series we formulate the concept of renyi s transfer entropy as a measure of information that is transferred only between certain parts of underlying distributions this is particularly pertinent in financial time series where the knowledge of marginal events such as spikes or sudden jumps is of a crucial importance we apply the renyian information flow to stock market time series from 11 world stock indices as sampled at a daily rate in the time period 02 01 1990 31 12 2009 corresponding heat maps and net information flows are represented graphically a detailed discussion of the transfer entropy between the dax and s p500 indices based on minute tick data gathered in the period 02 04 2008 11 09 2009 is also provided our analysis shows that the bivariate information flow between world markets is strongly asymmetric with a distinct information surplus flowing from the asia pacific region to both european and us markets an important yet less dramatic excess of information also flows from europe to the us this is particularly clearly seen from a careful analysis of renyi information flow between the dax and s p500 indices

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

reynolds averaged navier stokes computations of a flap side edge flowfield an extensive computational investigation of a generic high lift configuration comprising a wing and a half span flap reveals details of the mean flow field for flap deflections of 29 and 39 degrees the computational effort involves solutions of the thin layer form of the reynolds averaged navier stokes rans equations for both flap deflections the steady results show the presence of a dualvortex system a strong vortex forming on the lower portion of the flap side edge and a weaker one forming near the edge on the flap top surface downstream the vortex on the flap side edge grows and eventually merges with the vortex on the flap top surface comparison of on and off surface flow quantities with the experimental measurements of radeztsky singer and khorrami aiaa paper 98 0700 show remarkable agreement for the 39 degree flap deflection the calculation also reveals the occurrence of a vortex breakdown which is corroborated by 5 hole probe velocity measurements performed in the quiet flow facility at nasa langley the presence of the vortex breakdown significantly alters the flow field near the side edge

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

on the stability of generalized entropies by the use of a probabilistic coupling technique and generalizing a recent result of zhang 2007 lett math phys 80 171 we derive several sharp inequalities concerning the uniform continuity of some generalized entropies these inequalities capture certain aspects of the interplay between the entropies and the uniform distance variational distance and establish the stability of the involved entropies

generalized statistics yet another generalization we provide a unifying axiomatics for renyi s entropy and non extensive entropy of tsallis it is shown that the resulting entropy coincides with csiszar s measure of directed divergence known from communication theory

theory and numerical analysis of shells undergoing large elastic strains abstract a non linear bending theory of rubber like shells undergoing large elastic strains is proposed the theory is based on a relaxed normality hypothesis and the incompressibility condition using series expansion in the normal direction and applying some estimation technique a consistent first approximation and a simplest approximation to the elastic strain energy of the shell are constructed lagrangian displacement shell equations are derived and the incremental shell deformation is considered the numerical results presented for one and two dimensional large strain shell problems confirm the accuracy and efficiency of the proposed shell theory

towards information theory for q nonextensive statistics without q deformed distributions in this paper we extend our recent results p jizba t arimitsu physica a 340 2004 110 on q nonextensive statistics with non tsallis entropies in particular we combine an axiomatics of renyi with the q deformed version of khinchin axioms to obtain the entropy which accounts both for systems with embedded self similarity and q nonextensivity we find that this entropy can be uniquely solved in terms of a one parameter family of information measures the corresponding entropy maximizer is expressible via a special function known under the name of the lambert w function we analyze the corresponding high and low temperature asymptotics and make some remarks on the possible applications r 2006 elsevier b v all rights reserved

on a comparative study between dependence scales determined by linear and non linear measures in this manuscript we present a comparative study about the determination of the relaxation i e independence time scales obtained from the correlation function the mutual information and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy our results show that for systems with a small degree of complexity standard mutual information and the criterion based on its nonextensive generalisation provide the same scale whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller

prediction of high lift flows using turbulent closure models the flow over two different multi element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model a subset of recently measured transition locations using hot film on a mcdonnell douglas configuration is presented and the effect of transition location on the computed solutions is explored deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element and not necessarily inadequate turbulence modeling in the wake using measured transition locations for the main element improves the prediction of its boundary layer thickness skin friction and wake profile shape however using measured transition locations on the slat still yields poor slat wake predictions the computation of the slat flow field represents a key roadblock to successful predictions of multi element flows in general the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models

indices for testing neural codes one of the most critical challenges in systems neuroscience is determining the neural code a principled framework for addressing this can be found in information theory with this approach one can determine whether a proposed code can account for the stimulus response relationship specifically one can compare the transmitted information between the stimulus and the hypothesized neural code with the transmitted information between the stimulus and the behavioral response if the former is smaller than the latter i e if the code cannot account for the behavior the code can be ruled out the information theoretic index most widely used in this context is shannon s mutual information the shannon test however is not ideal for this purpose while the codes it will rule out are truly nonviable there will be some nonviable codes that it will fail to rule out here we describe a wide range of alternative indices that can be used for ruling codes out the range includes a continuum from shannon information to measures of the performance of a bayesian decoder we analyze the relationship of these indices to each other and their complementary strengths and weaknesses for addressing this problem

remarks on comments on on q non extensive statistics with non tsallisian entropy physica a 466 2017 160 abstract recently in ilic and stankovic 2017 have suggested that there may be problem for the class of hybrid entropies introduced in jizba and arimitsu 2004 in this comment we point out that the problem can be traced down to the q additive entropic chain rule and to a peculiar behavior of the de finetti kolmogorov relation for escort distributions however despite this one can still safely use the proposed hybrid entropies in most of the statistical thermodynamics considerations

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

navier stokes computations of vortical flows over low aspect ratio wings an upwind biased finite volume algorithm is applied to the low speed laminar flow over a low aspect ratio delta wing from 0 to 40 deg angle of attack the differencing is second order accurate spatially and a multigrid algorithm is used to promote convergence to the steady state the results compare well with the detailed experiments of hummel and others for an ret of 0 95 x 106 the predicted maximum lift coefficient of 1 10 at 35 deg angle of attack agrees closely with the measured maximum lift of 1 06 at 33 deg at 40 deg angle of attack a bubble type of vortex breakdown is evident in the computations extending from 0 6 of the root chord to just downstream of the trailing edge

nonequilibrium statistical operator method in renyi statistics abstract the generalization of the zubarev nonequilibrium statistical operator nso method for the case of renyi statistics is proposed when the relevant statistical operator or distribution function is obtained based on the maximum entropy principle for the renyi entropy the nonequilibrium statistical operator and corresponding generalized transport equations for the reduced description parameters are obtained a consistent description of the kinetic and hydrodynamic processes in a system of interacting particles is considered as an example

diffusion on fractal phase spaces and entropy production abstract complex systems may show strongly non exponential relaxation the origins of these behavior seem to be related to the fractal structure of the phase space in this article we consider the diffusion on a dilute hypercube this stochastic process is a coarse grained model for the time evolution of a glassy system where both the dynamics and the structure of the phase space was considered as simple as possible we characterize this process using two quantities a memory function and the tsallis entropy the first one is a measure of mixing while the second is related to non extensivity we characterize quantitatively their relationship finally we discuss the implications for other glassy and complex systems

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

solution of fractional kinetic equation by a class of integral transform of pathway type solutions of fractional kinetic equations are obtained through an integral transform named p transform introduced in this paper the p transform is a binomial type transform containing many class of transforms including the well known laplace transform the paper is motivated by the idea of pathway model introduced by mathai linear algebra appl 396 317 328 2005 10 1016 j laa 2004 09 022 the composition of the transform with differential and integral operators are proved along with convolution theorem as an illustration of applications to the general theory of differential equations a simple differential equation is solved by the new transform being a new transform the p transform of some elementary functions as well as some generalized special functions such as h function g function wright generalized hypergeometric function generalized hypergeometric function and mittag leffler function are also obtained the results for the classical laplace transform is retrieved by letting 1

zeroth law compatibility of nonadditive thermodynamics nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules corrected in this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics we find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these our result offers a possible solution to the long standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

conditional renyi entropies there is no generally accepted definition of conditional renyi entropy the unconditional renyi entropy depends on a parameter which for the case of min entropy takes the value even for this particular case there are several proposals for the definition of conditional entropy this paper describes three general definitions of conditional renyi entropy that were found or suggested in the literature their properties are studied and their values as a function of are compared the particular case of min entropy is widely used in cryptography as a security parameter this case is studied in some detail

multigrid and upwind viscous flow solver on three dimensional overlapped and embedded grids a computationally efficient method is presented for solving the three dimensional governing equations of the viscous compressible flows about complex configurations with geometrically nonsimilar components the physical domain is decomposed into regions for which the grid generation is relatively simple and virtually without significant restrictions the navier stokes equations are solved by an implicit upwind finite volume scheme the convergence is accelerated by a multigrid algorithm despite the holes created in the computational domain by the overlapped grids which are completely or partially embedded within one another the block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the existence of such holes the method is tested through two demonstrative csises the solution for a supersonic flow past a blunt nose cylinder at a high angle of attack is obtained using a c o grid embedded in a global cartesian grid this solution is successfully compared with the one obtained using a single c o grid and the experimental data then supersonic interference flows past an ogive nose cylinder in the close proximity of a flat plate are solved using overlapped and topologically nonsimilar but simple grids

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

irreversibility entropy and incomplete information abstract the open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a p a measure but the p a measure is not yet known consequently it is difficult to develop the statistical thermodynamics for an irreversible system here its integral expression is obtained in order to its use in the statistical thermodynamic analysis of the complex and irreversible systems

q exponential weibull and q weibull distributions an empirical analysis abstract in a comparative study the q exponential and weibull distributions are employed to investigate frequency distributions of basketball baskets cyclone victims brand name drugs by retail sales and highway length in order to analyze the intermediate cases a distribution the q weibull one which interpolates the q exponential and weibull ones is introduced it is verified that the basketball baskets distribution is well described by a q exponential whereas the cyclone victims and brand name drugs by retail sales ones are better adjusted by a weibull distribution on the other hand for highway length the q exponential and weibull distributions do not give satisfactory adjustment being necessary to employ the q weibull distribution furthermore the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law q exponential with q 1 controversy

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

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

comments on on q non extensive statistics with non tsallisian entropy abstract recently in jizba and korbel 2016 four generalized shannon khinchin gsk axioms have been proposed and a generalized entropy which uniquely satisfies the gsk axioms has been derived in this comment we show that the unique class of the entropies derived in the aforementioned paper is not correct as it violates the fourth gsk axiom and we derive the correct one nevertheless the class of entropies proposed in the commented paper still can serve as a basis for generalized statistical mechanics we propose a new axiomatic system which characterizes the class of entropies

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems

reynolds stress model dual time stepping computation of unsteady three dimensional flows an efficient and robust implicit methodology for the integration of the unsteady three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynolds stress closure is developed the five mean flow and seven turbulence transport equations are discretized on a structured deforming grid using an o x 3 finite volume upwind biased muscl scheme time integration uses an implicit o t 2 dual time stepping procedure with alternating direction implict subiterations with approximate jacobians designed to minimize the computing time requirements of the implicit phase for the reynolds stresses so that the computational overhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration based on a dynamic criterion of subiterative convergence grid deformation velocities associated with solid wall displacement are computed using a laplacian operator the method is validated by comparison with experimental data for 1 two dimensional pitching oscillations of a naca 0012 airfoil and 2 three dimensional shock wave oscillation in a transonic channel the influence of the various parameters of the method is analyzed in detail

new strategy for assumed stresses for 4 node hybrid stress membrane element an oblique skew co ordinate system defined at the origin of the isoparametric co ordinates is introduced as the reference co ordinate system for assumed stresses in the formulation of a 4 node hybrid membrane element the initially uncoupled stresses in these reference co ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of pian and wu7 when suitable incompatible displacements are introduced such strategy allows the element stiffness to be formulated by using either the hellinger reissner or the complementary energy functional numerical results show that the performances of three elements constructed by using different sets of incompatible displacements in this paper are practically identical and are all of slightly higher accuracy than that of the pian sumihara element6

roundoff induced attractors and reversibility in conservative two dimensional maps we numerically study two conservative two dimensional maps namely the baker map whose lyapunov exponent is known to be positive and a typical one exhibiting a vanishing lyapunov exponent chosen from the generalized shift family of maps introduced by c moore phys rev lett 64 1990 2354 in the context of undecidability we calculate the time evolution of the entropy sq 1 i 1wpiq q 1 s1 sbg i 1wpilnpi we exhibit the dramatic effect introduced by numerical precision indeed in spite of being area preserving maps they present well after the initially concentrated ensemble has spread virtually all over the phase space unexpected pseudo attractors fixed point like for the baker map and more complex structures for the moore map these pseudo attractors and the apparent time partial reversibility they provoke gradually disappear for increasingly large precision in the case of the moore map they are related to zero lebesgue measure effects associated with the frontiers existing in the definition of the map in addition to the above and consistent with the results by v latora and m baranger phys rev lett 82 1999 520 we find that the rate of the far from equilibrium entropy production of baker map numerically coincides with the standard kolmogorov sinai entropy of this strongly chaotic system

a tsallis statistics based neural network model for novel word learning abstract we invoke the tsallis entropy formalism a nonextensive entropy measure to include some degree of non locality in a neural network that is used for simulation of novel word learning in adults a generalization of the gradient descent dynamics realized via nonextensive cost functions is used as a learning rule in a simple perceptron the model is first investigated for general properties and then tested against the empirical data gathered from simple memorization experiments involving two populations of linguistically different subjects numerical solutions of the model equations corresponded to the measured performance states of human learners in particular we found that the memorization tasks were executed with rather small but population specific amounts of nonextensivity quantified by the entropic index q our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems