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

properties of the non extensive gaussian entropy the present work investigates the lesche stability experimental robustness the thermodynamic stability the legendre structure of thermodynamics and derives the maximum entropy distribution of the one parametric non extensive gaussian entropy we show that this entropy definition fulfills both stability conditions for all values of its parameter q r the entropy maximizer contains the lambert w function which allows the preservation of the legendre transformations

κ deformed fourier transform abstract we present a new formulation of fourier transform in the picture of the algebra derived in the framework of the generalized statistical mechanics the fourier transform is obtained from a fourier series recently introduced by scarfone 2013 the kernel of this transform that reduces to the usual exponential phase in the 0 limit is composed by a deformed phase and a damping factor that gives a wavelet like behaviour we show that the fourier transform is isomorph to the standard fourier transform through a changing of time and frequency variables nevertheless the new formalism is useful to study according to fourier analysis those functions defined in the realm of the algebra as a relevant application we discuss the central limit theorem for the sum of n iterate statistically independent random variables

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

stability of incomplete entropy and incomplete expectation region des pays de la loire of france 2007 6088 science research fund 07bs105 huaqiao university people s republic of china

temporal extensivity of tsallis entropy and the bound on entropy production rate the tsallis entropy which is a generalization of the boltzmann gibbs entropy plays a central role in nonextensive statistical mechanics of complex systems a lot of efforts have recently been made on establishing a dynamical foundation for the tsallis entropy they are primarily concerned with nonlinear dynamical systems at the edge of chaos here it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by carati a carati physica a 348 110 2005 that whenever relevant the tsallis entropy indexed by q is temporally extensive linear growth in time i e finite entropy production rate then the universal bound on the entropy production rate is shown to be 1 absolute value 1 q the property of the associated probabilistic process i e the sojourn time distribution determining randomness of motion in phase space is also analyzed

deriving partition functions and entropic functionals from thermodynamics abstract given an arbitrary probability distribution and a nondegenerate energy spectrum so that a mean energy u can be computed we derive the partition function z and the entropic functional s that satisfy the basic relation d u t d s the procedure is illustrated by considering examples of typical distributions found currently in nature in particular the power law spectrum is shown to correspond to a critical state associated with tsallis entropy

a counterexample against the lesche stability of a generic entropy functional region des pays de la loire of france 2007 6088 2007 11953 huaqiao university people s republic of china 07bs105 ismans

how should the distance of probability assignments be judged it is shown that the l1 distance in the space of probability assignments on a finite set provides a criterion to judge whether two assignments are too close to each other to be distinguished by a statistical test the criterion is independent of the number of elements of other notions of distance are also discussed

invertible linear maps on borel subalgebras preserving zero lie products abstract let g be a simple lie algebra of rank l over an algebraically closed field of characteristic zero b a borel subalgebra of g an invertible linear map on b is said preserving zero lie products in both directions if for x y b x y 0 if and only if x y 0 in this paper it is shown that an invertible linear map on b preserving zero lie products in both directions if and only if it is a composition of an inner automorphism a graph automorphism a scalar multiplication map and a diagonal automorphism which extends the main result in 8 from a linear solvable lie algebra to far more general cases

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

legendre structure of κ thermostatistics revisited in the framework of information geometry information geometry is a powerful framework in which to study families of probability distributions or statistical models by applying differential geometric tools it provides a useful framework for deriving many important structures in probability theory by identifying the space of probability distributions with a differentiable manifold endowed with a riemannian metric in this paper we revisit some aspects concerning the thermostatistics based on the entropy s in the framework of information geometry after introducing the dually flat structure associated with the distribution we show that the dual potentials derived in the formalism of information geometry correspond to the generalized massieu function and the generalized entropy s characterizing the legendre structure of the deformed statistical mechanics in addition we obtain several quantities such as escort distributions and canonical divergence relevant for the further development of the theory

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

steady infiltration flows with sloping boundaries general theorems are established that enable immediate solution of the quasilinear steady infiltration equation for any distribution of line and point sources at or beneath a sloping upper soil surface or on or above a sloping impermeable base the required solutions are readily deduced from the known simple solutions for buried line and point sources corollary to the theorems similar relations hold for downslope and cross slope flux density components illustrative solutions are presented for line and point sources in the various configurations distributions of both potential and stream function are mapped for line sources and also for point sources at or beneath a horizontal surface for other point sources potential is mapped in the normal plane through the source for sources beneath a surface distortion due to the surface is relatively small even for dimensionless normal source depth as small as 1 on the other hand for sources above a sloping base the base strongly skews the distributions of both potential and streamlines far downslope the flow is purely line sources or primarily point sources parallel to the base upper bounds exist on total source strength beyond which a saturated region emerges perched on a horizontal base consistent with earlier results and theorems physically acceptable steady flows do not exist above the base

group entropies correlation laws and zeta functions the notion of group entropy is proposed it enables the unification and generaliztion of many different definitions of entropy known in the literature such as those of boltzmann gibbs tsallis abe and kaniadakis other entropic functionals are introduced related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium when the dynamics is weakly chaotic the associated thermostatistics are discussed the mathematical structure underlying our construction is that of formal group theory which provides the general structure of the correlations among particles and dictates the associated entropic functionals as an example of application the role of group entropies in information theory is illustrated and generalizations of the kullback leibler divergence are proposed a new connection between statistical mechanics and zeta functions is established in particular tsallis entropy is related to the classical riemann zeta function

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 one parameter deformation of the exponential function abstract recently in kaniadakis physica a 296 2001 405 a new one parameter deformation for the exponential function exp x 1 2 x 2 x 1 exp 0 x exp x which presents a power law asymptotic behaviour has been proposed the statistical distribution f z 1 exp e has been obtained both as stable stationary state of a proper nonlinear kinetics and as the state which maximizes a new entropic form in the present contribution starting from the algebra and after introducing the analysis we obtain the exponential exp x as the eigenstate of the derivative and study its main mathematical properties

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

generalized entropies and the transformation group of superstatistics superstatistics describes statistical systems that behave like superpositions of different inverse temperatures so that the probability distribution is where the kernel f is nonnegative and normalized f d 1 we discuss the relation between this distribution and the generalized entropic form the first three shannon khinchin axioms are assumed to hold it then turns out that for a given distribution there are two different ways to construct the entropy one approach uses escort probabilities and the other does not the question of which to use must be decided empirically the two approaches are related by a duality the thermodynamic properties of the system can be quite different for the two approaches in that connection we present the transformation laws for the superstatistical distributions under macroscopic state changes the transformation group is the euclidean group in one dimension

a theorem on the existence of trace form generalized entropies an analytic technique is proposed which allows to generate many new examples of entropic functionals generalizing the standard boltzmanngibbs entropy our approach is based on the existence of a g

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

thermodynamic stabilities of the generalized boltzmann entropies abstract we consider the thermodynamic stability conditions tsc on the boltzmann entropies generalized by tsallis q and kaniadakis deformed logarithmic functions it is shown that the corresponding tscs are not necessarily equivalent to the concavity of the generalized boltzmann entropies with respect to internal energy nevertheless both the tscs are equivalent to the positivity of standard heat capacity

microcanonical foundation for systems with power law distributions starting from a microcanonical basis with the principle of equal a priori probability it is shown using the method of steepest descents that besides ordinary boltzmann gibbs theory with the exponential distribution a theory describing systems with power law distributions can also be derived

stochastic analysis of field measured unsaturated hydraulic conductivity unsaturated hydraulic conductivity k values as a function of soil water pressure head h were measured in the soil at 75 cm depth at 70 different sites separated from one another by a distance of l m along a horizontal transect k field was viewed as a random function of spatial location x field data were analyzed 1 to examine the isotropy and stationarity of k 2 to check the ergodicity of k in the mean and covariance functions and 3 to characterize the distribution properties of k by estimating the higher order correlations that is third and fourth cumulants the mean functions were estimated by averaging over h and x the covariance function was studied to investigate its spatial origin dependency logs and square roots of k were used for estimating the third and fourth cumulants results showed that spatial covariance functions are anisotropic and both lag and origin dependent that is spatially nonhomogeneous because the stationarity statistical homogeneity of k is scale dependent which was indicated by the identification of locally stationary covariance regions the ergodic properties of k are also scale dependent at smaller spatial scales results related to the distribution characteristics of k indicated that although ln k is marginally gaussian distributed in the context of spatial stochastic processes the random field of ln k is not gaussian because the third and fourth cumulants of the field are still significantly different from zero and have the same order of magnitude as the first and second cumulants the square root transformation however resulted in a random field that is approximately gaussian although marginal distributions of k remained skewed analyses of ln k and k indicated that better transformations which would result in both marginal and joint gaussian behavior for the random field of k are needed

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

a geostatistical approach to the trickle irrigation design in heterogeneous soil 1 theory a geostatistical approach was used to investigate the spatial variability of two measured soil hydraulic parameters the saturated hydraulic conductivity ks and d log k h d h where k is the hydraulic conductivity and h is the soil water pressure head using a linearized solution to steady infiltration from a circular shallow pond the spatial distribution of the midway soil water pressure head between emitters hc for a given trickle discharge rate q and spacing between emitters d was calculated using the spatially variable soil parameters ks and the spatial distribution of the crop yield y was calculated from the spatially variable hc by using a quadratic expression for the y hc relationships it was found that the spatial variability of each of the measured input parameters ks and or the calculated output variables hc and y is expressed through the variogram and can be characterized in terms of the coefficient of variation cv and the integral scale j in the case of log ks for which the sill is reached at relatively small range two different were tested results showed that the kriged values of log ks as well as the resultant values of hc hc ks d q were relatively insensitive to the selected the spatial variability of hc reduced the average over the field crop yield that would have been obtained when hc was uniform throughout the field the spatially variable soil parameters ks and were used to calculate the spatial distribution of the spacing between emitters d required to achieve for a given trickle discharge a prespecified value of hc uniform throughout the field it was found that the use of a spatially variable d increased the field crop yield by 3 relative to the yield that was obtained when a single valued d uniform throughout the field was used the spatial distribution of d was combined with hydraulic principles to derive the spatial distribution of lateral diameter and length for engineering design requirements

what happens near a quasi linear point source the quasi linear continuous point source has been central to many studies of multidimensional flow in unsaturated soil immediately next to the source however the water pressure is positive and indefinitely large so the quasi linear flow equation limited to 0 fails in principle we investigate whether this is a serious problem in practice exact analysis would be complicated and difficult since the problem is of mixed saturated unsaturated flow with an unknown free boundary between the two regions when the source strength is not too large the saturated region is close to spherical a simple approximate analysis follows with exterior and interior flow velocities matched on the boundary the correction taking into account the saturated region shifts the quasi linear source a small distance above the actual source location in practical applications the correction is usually negligibly small physical reasons why the approximation works well and the correction is small are indicated in addition these physical reasons suggest that the scope of the quasi linear analysis is wider than supposed hitherto the solution in potential theory for the eccentric point source needed for the study is given in the appendix

general exact solution to the problem of the probability density for sums of random variables the exact explicit expression for the probability density p n x for a sum of n random arbitrary correlated summands is obtained the expression is valid for any number n and any distribution of the random summands most attention is paid to application of the developed approach to the case of independent and identically distributed summands the obtained results reproduce all known exact solutions valid for the so called stable distributions of the summands it is also shown that if the distribution is not stable the profile of p n x may be divided into three parts namely a core small x a tail large x and a crossover from the core to the tail moderate x the quantitative description of all three parts as well as that for the entire profile is obtained a number of particular examples are considered in detail

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

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

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

on the stability of analytic entropic forms abstract the stability against small perturbations on the probability distributions also called experimental robustness of analytic entropic forms is analyzed entropies s p associated with a given set of probabilities p i that can be written in the simple form s p i 1 w r p i are shown to be robust if r p i is an analytic function of the p i s the same property holds for entropies s p that are monotonic and analytic functions of s p the tsallis entropy s q p falls in the first class of entropies whenever the entropic index q is an integer greater than 1 a new kind of entropy that follows such requirements is discussed

a geostatistical approach to the trickle irrigation design in a heterogeneous soil 2 a field test in a heterogeneous field in which the soil water properties vary under a deterministic uniform trickle irrigation system the midway soil water pressure head hc and the yield of a crop also differ from place to place these differences may in turn reduce the average over the field yield relative to the yield that would be obtained if the soil was uniform throughout the field a field experiment was conducted to test the hypothesis that this yield reduction may be eliminated by using a spatially variable trickle irrigation system twenty five plots 200 m2 each were established on a 30 m2 grid half of each plot was equipped with a standard trickle irrigation system with constant spacing between emitters of d 50 cm control plots and the other half was equipped with a trickle irrigation system for which the spacing between the emitters was selected by using the pertinent hydraulic properties the saturated hydraulic conductivity ks and the soil parameter according to the procedure of bresler 1978 as described in paper 1 russo 1983b values of hc measured at different times as well as the total fruit yield y of bell pepper capsicum frutescens var maor were used to estimate the seasonal and the spatial distributions of hc and the spatial distribution of y and their moments the variograms of hc and y were calculated and used to estimate their integral scales it was found that the use of a spatially variable d relative to the use of a uniform d did not change the seasonal behavior of hc but reduced the spatial variability in hc and y by 35 and 11 respectively and increased the integral scale of hc and y by 30 and 10 respectively but increased the average total fruit yield by only 1 9 the use of a spatially variable d reduced the dependence of y on hc this indicates that when the emitters are properly spaced it is not the water but other factors that most influence yield when a constant d was used the dependence of y of hc decreased with time this and the relatively good agreement between the values of hc measured at the initial stages of the growing season and those calculated in paper 1 demonstrate that the concept of hc is important in the early stages of the plant s growth when the root system is not fully developed both the theoretical paper 1 and the experimental results showed that although ks and as well as hc varied considerably in the field the spatial variability of the crop yield was relatively small this explains why the use of a spatially variable d essentially was not an improvement over the fixed d it is suggested that this study will be considered as a methodological one which can be adapted to solve practical problems associated with field spatial variability

generalized entropy optimized by a given arbitrary distribution an ultimate generalization of the maximum entropy principle is presented an entropic measure which is optimized by a given arbitrary distribution with the finite linear expectation value of a physical random quantity of interest is constructed it is concave irrespective of the properties of the distribution and satisfies the h theorem for the master equation combined with the principle of microscopic reversibility this offers a unified basis for a great variety of distributions observed in nature as examples the entropies associated with the stretched exponential distribution postulated by anteneodo and plastino 1999 j phys a math gen 32 1089 and the deformed exponential distribution by kaniadaki 2002 phys rev e 66 056125 and naudts 2002 physica a 316 323 are derived to include distributions with divergent moments e g the levy stable distributions it is necessary to modify the definition of the expectation value

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

conditional stochastic averaging of steady state unsaturated flow by means of kirchhoff transformation we consider the effect of measuring randomly varying soil hydraulic properties on one s ability to predict steady state unsaturated flow subject to random sources and or initial and boundary conditions our aim is to allow optimum unbiased prediction of system states pressure head water content and fluxes deterministically without upscaling and without linearizing the constitutive characteristics of the soil it has been shown by neuman et al 1999 that such prediction is possible by means of first ensemble moments of system states and fluxes conditioned on measured values of soil properties when the latter scale in a linearly separable fashion as proposed by vogel et al 1991 the uncertainty associated with such predictions can be quantified by means of the corresponding conditional second moments the derivation of moment equations for soils whose properties do not scale in the above manner requires linearizing the corresponding constitutive relations which may lead to major inaccuracies when these relations are highly nonlinear as is often the case in nature when the scaling parameter of pressure head is a random variable independent of location the steady state unsaturated flow equation can be linearized by means of the kirchhoff transformation for gravity free flow linearization is also possible in the presence of gravity when hydraulic conductivity varies exponentially with pressure head for the latter case we develop exact conditional first and second moment equations which are nonlocal and therefore non darcian we solve these equations analytically by perturbation for unconditional vertical infiltration and compare our solution with the results of numerical monte carlo simulations our analytical solution demonstrates in a rigorous manner that the concept of effective hydraulic conductivity does not apply to ensemble averaged unsaturated flow except when gravity is the sole driving force

the quasilinear approximation for unsaturated porous media flow this paper gives a review of the quasilinear approximation an exponential relationship between hydraulic conductivity and moisture potential and the uses this has been put to since the time of its creation one of the major attractions of this approximation is that under steady regimes the highly nonlinear richards equation governing unsaturated flow can be linearized this simplification has enabled analytic and semianalytic solutions to be found for many unsaturated flow problems these are reviewed and the current research areas in which the quasilinear approximation is being used are discussed

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

thermodynamic equilibrium and its stability for microcanonical systems described by the sharma taneja mittal entropy it is generally assumed that the thermodynamic stability of equilibrium states is reflected by the concavity of entropy we inquire in the microcanonical picture about the validity of this statement for systems described by the two parametric entropy s kappa r of sharma taneja and mittal we analyze the composability rule for two statistically independent systems a and b described by the entropy s kappa r with the same set of the deformation parameters it is shown that in spite of the concavity of the entropy the composability rule modifies the thermodynamic stability conditions of the equilibrium state depending on the values assumed by the deformation parameters when the relation s kappa r a union b s kappa r a s kappa r b holds superadditive systems the concavity condition does imply thermodynamics stability otherwise when the relation s kappa r a union b s kappa r a s kappa r b holds subadditive systems the concavity condition does not imply thermodynamical stability of the equilibrium state

infiltration from a surface point source and drip irrigation 1 the midpoint soil water pressure bresler 1978 proposed a procedure for drip irrigation design which is focused on the midpoint soil water pressure hc we present a practical field test of this approach in order to evaluate the validity of the underlying assumptions the simulated hc values were obtained from raats 1971 steady state theory for 32 points in the field where the hydraulic conductivity parameters ks and were measured the hc values were measured at the same locations during microirrigation of a maize crop measured hc s appear to be lower than the simulated ones especially late in the season the measured spatial variability in hc appeared to be higher than the simulated ones this could well have been caused by root uptake activity which is not considered in the analysis as well as by the large but typical drippers spacing of d 1 00 m thus the tensiometers could have been beyond the practical limit of wetting consequences for design and management are important for design even if a high hc value is chosen there is no real guarantee that the wetting would be effective at the midpoint for irrigation management tensiometer placement too far from the dripper would lead to overirrigation so for a large dripper spacing d the midpoint placement is not judicious

a possible deformed algebra and calculus inspired in nonextensive thermostatistics we present a deformed algebra related to the q exponential and the q logarithm functions that emerge from nonextensive statistical mechanics we also develop a q derivative and consistently a q integral for which the q exponential is an eigenfunction the q derivative and the q integral have a dual nature that is also presented

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

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

a κ entropic approach to the analysis of the fracture problem abstract in order to study the relation between the ohmic resistance measured in a thin conducting ribbon and the length of a transversal cut we employ a one parameter deformed exponential and logarithm that were recently introduced phys rev e 66 2002 056125 in the framework of a generalized statistical mechanics the analytical results have been compared with the data that was experimentally obtained and numerically computed with the boundary element method remarkably the new deformed functions that interpolate between the standard functions and the power law functions allow the best fit of the experimental data to be obtained for a wide range of the cut length

remarks about the tsallis formalism in the present paper the conditions for the validity of the tsallis statistics are analyzed the same has been done following the analogy with the traditional case starting from the microcanonical description of the systems and taking into account their self similarity scaling properties in the thermodynamic limit it is analyzed the necessary conditions for the equivalence of microcanonical ensemble with the tsallis generalization of the canonical ensemble it is shown that the tsallis statistics is appropriate for the macroscopic description of systems with potential scaling laws of the asymptotic accessible states density of the microcanonical ensemble our analysis shows many details of the tsallis s formalism the q expectation values the generalized legendre transformations between the thermodynamic potentials as well as the conditions for its validity having a priori the possibility to estimate the value of the entropic index without the necessity of appealing to the computational simulations or the experiment on the other hand the definition of physical temperature received a modification that differs from the toral result for the case of finite systems we have generalized the microcanonical thermostatistics of gross with the generalization of the curvature tensor for this kind of description

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

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

real structures on rational surfaces and automorphisms acting trivially on picard groups in this article we prove that any complex smooth rational surface x which cannot be obtained by blowing up mathbb p 2 mathbb c at r geq 10 points has a finite number of real forms owing to simple results about the group mathrm aut x of complex automorphisms of x which act trivially on the picard group of x

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

infiltration in stratified heterogeneous soils relative importance of parameters and model variations 1 this study presents a framework that accounts for the uncertainty relative importance and relative contribution of uncertain and spatially variable parameters and the influence of statistical model assumptions in problems of infiltration in unsaturated heterogeneous formations the relative importance of the saturated hydraulic conductivity k s the van genuchten and 3 parameters was quantified toward the mean pressure head profile and the fluctuations about it the broad implications of our study for site characterizations efforts are the following statistical moments were seen not to be sufficient for producing reliable modeling estimates significant information on the detailed shape of the probability distribution is required in order to produce meaningful predictions when limited data are available optimum allocation of resources is accomplished by concentrating on k s when more extensive sampling can be done both k s and appear to be critical total system performance analyses may not provide the most appropriate modeling estimates the results of the relative importance of the parameters for a specific layer did not coincide with the conclusions drawn from an analysis of the system as a whole

multidimensional steady infiltration to a water table we address the question of the applicability of the body of solutions for quasi linear multidimensional steady infiltration with perfect drainage to cases with a water table or by inference a sloping impermeable base at a finite depth beneath the water supply source the exact solutions for steady quasi linear point and line sources over a water table are our point of departure with their aid we construct approximate solutions to the general problem of three dimensional axisymmetric and two dimensional steady infiltration from finite water supply sources at fixed moisture potential to a water table at finite depth we take as illustrative solutions disc and strip shaped water supply sources when the depth from the source to the water table or the base is of order 4 sorptive lengths perfect drainage solutions yield discharge estimates of ample accuracy when the depth is less our approximate analysis gives in favorable cases the requisite correction in less favorable cases it gives the order of magnitude of the correction the study is facilitated by a method of exponentially weighted images applicable to the quasi linear flow equation

maximum entropy approach to stretched exponential probability distributions we introduce a nonextensive entropy functionals whose optimization under simple constraints mean values of some standard quantities yields stretched exponential probability distributions which occur in many complex systems the new entropy functional is characterized by a parameter the stretching exponent such that for d 1 the standard logarithmic entropy is recovered we study its mathematical properties showing that the basic requirements for a well behaved entropy functional are verified i e s possesses the usual properties of positivity equiprobability concavity and irreversibility and verifies khinchin axioms except the one related to additivity since s is nonextensive the entropys is shown to be superadditive for 1

statistical descriptions of nonlinear systems at the onset of chaos abstract ensemble of initial conditions for nonlinear maps can be described in terms of entropy this ensemble entropy shows an asymptotic linear growth with rate k the rate k matches the logarithm of the corresponding asymptotic sensitivity to initial conditions the statistical formalism and the equality k can be extended to weakly chaotic systems by suitable and corresponding generalizations of the logarithm and of the entropy using the logistic map as a test case we consider a wide class of deformed statistical description which includes tsallis abe and kaniadakis proposals the physical criterion of finite entropy growth k strongly restricts the suitable entropies we study how large is the region in parameter space where the generalized description is useful

some groups of type vf a group is of type vf if it contains a finite index subgroup which has a finite classifying space we construct groups of type vf in which the centralizers of some elements of finite order are not of type vf and groups of type vf containing infinitely many conjugacy classes of finite subgroups from these examples it follows that a group g of type vf need not admit a finite type or finite classifying space for proper actions sometimes also called the universal proper g space we construct groups g for which the minimal dimension of a universal proper g space is strictly greater than the virtual cohomological dimension of g each of our groups embeds in some general linear group over the rational integers applications to algebraic k theory of group algebras and topological k theory of group c algebras are also considered the groups are constructed as finite extensions of bestvina brady groups

on a q generalization of circular and hyperbolic functions a generalization of the circular and hyperbolic functions is proposed based on the tsallis statistics and on a consistent generalization of the euler formula some properties of the presently proposed q trigonometry are then investigated the generalized functions are exact solutions of a nonlinear oscillator original circular and hyperbolic relations are recovered as the limiting case

algebra and calculus for tsallis thermo statistics abstract we construct generalized additions and multiplications forming fields and division algebras inspired by the tsallis thermo statistics we also construct derivations and integrations in this spirit these operations do not reduce to the naively expected ones when the deformation parameter approaches zero

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators