a thermodynamic like approach for the study of probabilistic systems abstract this paper starts by considering an arbitrary system for which the probability distribution p p 1 p 2 p n of a measurable property with n possible independent results is known by using the hartley information pseudo energy the escort probabilities of p and its shannon entropy a thermodynamic like formalism is developed including the deduction of the fundamental equation for the mean value of the pseudo energies thus the method allows a macrodescription of the system that is based on a purely mathematical procedure and involves thermodynamic like variables as a specific example we consider a bank that measures customer satisfaction by doing a statistical survey satisfied or unsatisfied customers

a study of convergence on the newton homotopy continuation method the traditional newton method is a well known and popular method for solving non linear equation it has high efficient in the convergence speed however we always need to guess the initial value in the iteration process good initial guess value can solve the equation quickly bad initial guess value usually will yield divergence homotopy continuation method is a kind of perturbation method it can guarantee the answer by a certain path if we choose the auxiliary homotopy function or call start system well this paper presents some useful rules for the choice of the auxiliary homotopy function to avoid the problem of divergence of traditional newton method

a theorem on the equilibrium thermodynamics of hamiltonian systems we prove a theorem stating that within an interesting class of stationary solutions of the liouville equation the tsallis q distributions are the only ones that satisfy a condition which guarantees the existence of an integrating factor for the heat the functional forms of the distribution as well as that of entropy temperature and heat capacity are derived we then explain why the gibbs distribution as a limit of the tsallis one plays a privileged role for large size ordinary molecular systems

new iterative technique for solving nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the nonlinear equations in this paper a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique the convergence of the proposed methods is proved it is shown that the new family contains several well known iterative methods as special case for the implementation and performance of the new methods a nonlinear equation arising in the population model and another one arising in the motion of a particle on inclined plane is solved

some multi step iterative methods for solving nonlinear equations in this paper we develop some new iterative methods for solving nonlinear equations by using the techniques introduced in golbabai and javidi 2007 1 and rafiq and rafiullah 2008 20 we establish the convergence analysis of the proposed methods and then demonstrate their efficiency by taking some test problems

homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative abstract in this paper homotopy perturbation method is directly extended to investigate nonlinear coupled equations with parameters derivative and to derive their numerical solutions these nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations by choosing different values of the parameters in general formal numerical solutions as a result a very rapidly convergent series solution is obtained the efficiency and accuracy of the method are verified by using two famous examples coupled burgers and mkdv equations numerical solutions show that good results have been achieved

effectiveness of the kozachenko leonenko estimator for generalized entropic forms in this brief report we discuss the effectiveness of the kozachenko leonenko entropy estimator when generalized to cope with entropic forms customarily applied to study systems evincing asymptotic scale invariance and dependence either of linear or nonlinear kind we show that when the variables are independently and identically distributed the estimator is only valuable along the whole domain if the data follow the uniform distribution whereas for other distributions the estimator is only effectual in the limit of the boltzmann gibbs shanon entropic form we also analyze the influence of the dependence linear and nonlinear between variables on the accuracy of the estimator between variables as expected in the last case the estimator loses efficiency for the boltzmann gibbs shanon entropic form as well

a closer look at the indications of q generalized central limit theorem behavior in quasi stationary states of the hmf model abstract we give a closer look at the central limit theorem clt behavior in quasi stationary states of the hamiltonian mean field model a paradigmatic one for long range interacting classical many body systems we present new calculations which show that following their time evolution we can observe and classify three kinds of long standing quasi stationary states qss with different correlations the frequency of occurrence of each class depends on the size of the system the different microscopic nature of the qss leads to different dynamical correlations and therefore to different results for the observed clt behavior

a new hybrid iteration method for solving algebraic equations abstract a new hybrid iteration method the hybrid s name was used by luo xing guo luo applied mathematics and computation 171 2 2005 1171 1183 has been proposed for solving a non linear algebraic equation f x 0 by using taylor s theorem in this paper we proposed a new hybrid iteration method and we show by one equation that this new hybrid iteration method is more quickly convergent than newton s method and hence than hybrid iteration method

the solution of multipoint boundary value problems by the optimal homotopy asymptotic method in this work we solve multipoint boundary value problems using the optimal homotopy asymptotic method oham the proposed method is tested upon several problems from the literature and the results are compared with the available exact solution this method provides easy tools to control the convergence region of approximating solution series where ever necessary

a new iteration method for solving algebraic equations in this paper a nonlinear algebraic equation f x 0 by applying taylor s theorem is converted into a coupled iteration systeml x n 1 g x n 0andg x n f x n l x n wherel x ax 2 bx c the formula is of high convergence some examples are given

reciprocity relations and generalized classic entropic quantifiers that lack trace form abstract in this effort we show that the legendre reciprocity relations thermodynamics essential formal feature are respected by general classic entropic functionals even if they are not of trace form nature in contrast with shannon s or tsallis cases further with reference to the maximum entropy maxent variational process we encounter important cases relevant to physical applications currently discussed in the research literature in which the associated reciprocity relations exhibit anomalies we show that these anomalies can be cured by carefully discriminating between apparently equivalent entropic forms

a new iteration method with cubic convergence to solve nonlinear algebraic equations abstract in this paper a new iteration scheme is proposed to solve the roots of an algebraic equation f x 0 given an initial guess x0 the roots of the equation can be obtained using the following iteration scheme x n 1 x n f x n f 2 x n 2 f x n f x n f x n this iteration scheme has unique convergence characteristics different from the well known newton s method it is shown that this iteration method has cubic local convergence in the neighborhood of the root using this scheme real or complex roots for specific algebraic equations can be found because there are two iteration directions for a given initial guess two solutions can be found for certain algebraic equations with multiple roots examples are presented and compared with other methods

an efficient point algorithm for a linear two stage optimization problem this paper presents an algorithm using sensitivity analysis to solve a linear two stage optimization problem the underlying theory rests on a set of first order optimality conditions that parallel the kuhn tucker conditions associated with a one dimensional parametric linear program the solution to the original problem is uncovered by systematically varying the parameter over the unit interval and solving the corresponding linear program finite convergence is established under nondegenerate assumptions the paper also discusses other solution techniques including branch and bound and vertex enumeration and gives an example highlighting their computational and storage requirements by these measures the algorithm presented here has an overall advantage finally a comparison is drawn between bicriteria and bilevel programming and underscored by way of an example

on a new class of bilevel programming problems and its use for reformulating mixed integer problems abstract we extend some known results about the bilevel linear problem blp a hierarchical two stage optimization problem showing how it can be used to reformulate any mixed integer linear problem then we introduce some new concepts which might be useful to fasten almost all the known algorithms devised for blp as this kind of reformulation appears to be somewhat artificial we define a natural generalization of blp the bilevel linear quadratic problem bl qp and show that most of the exact and or approximate algorithms originally devised for the blp such as gsa or k th best can be extended to this new class of bilevel programming problems for bl qp more natural reformulations of mips are available leading to the use of known nonexact algorithms for blp as heuristic approaches to mips we report some contrasting results obtained in the network design problem case showing that although the direct application of our dual gsa algorithm is not of any practical use we obtain as a by product a good theoretical characterization of the optimal solutions set of the ndp along with a powerful scheme for constructing fast algorithms for the minimum cost flow problem with piecewise convex linear cost functions

computational difficulties of bilevel linear programming we show using small examples that two algorithms previously published for the bilevel linear programming problem blp may fail to find the optimal solution and thus must be considered to be heuristics a proof is given that solving blp problems is np hard which makes it unlikely that there is a good exact algorithm

application of the optimal homotopy asymptotic method to squeezing flow in this paper axisymmetric flow of two dimensional incompressible fluids is studied the optimal homotopy asymptotic method oham is applied to derive a solution of the reduced fourth order nonlinear boundary value problem for comparison the same problem is also solved by the perturbation method pm the homotopy perturbation method hpm 3 and the homotopy analysis method ham 4 oham is parameter free and provides better accuracy at lower order of approximation moreover we can easily adjust and control the convergence region as a result it is concluded that the new technique oham shows fast convergence simplicity of application and efficiency

statistical modelling of higher order correlations in pools of neural activity abstract simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles to understand how large ensembles of neurons process sensory information it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains using the information geometry framework it is possible to estimate higher order correlations by assigning one interaction parameter to each degree of correlation leading to a 2 n 1 dimensional model for a population with n neurons however this model suffers greatly from a combinatorial explosion and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach to quantify the extent of higher than pairwise spike correlations in pools of multiunit activity we use an information geometric approach within the framework of the extended central limit theorem considering all possible contributions from higher order spike correlations the identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher order correlations in the case of a very large neural ensemble significantly reducing the number of parameters avoiding the sampling problem and inferring the underlying dynamical properties of the network within pools of multiunit neural activity

computational applications of nonextensive statistical mechanics computational applications of the nonextensive entropy s q and nonextensive statistical mechanics a current generalization of the boltzmann gibbs bg theory are briefly reviewed the corresponding bibliography is provided as well

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

a parametric algorithm for convex cost network flow and related problems abstract the convex cost network flow problem is to determine the minimum cost flow in a network when cost of flow over each arc is given by a piecewise linear convex function in this paper we develop a parametric algorithm for the convex cost network flow problem we define the concept of optimum basis structure for the convex cost network flow problem the optimum basis structure is then used to parametrize v the flow to be transsshipped from source to sink the resulting algorithm successively augments the flow on the shortest paths from source to sink which are implicitly enumerated by the algorithm the algorithm is shown to be polynomially bounded computational results are presented to demonstrate the efficiency of the algorithm in solving large size problems we also show how this algorithm can be used to i obtain the project cost curve of a cpm network with convex time cost tradeoff functions ii determine maximum flow in a network with concave gain functions iii determine optimum capacity expansion of a network having convex arc capacity expansion costs

new family of iterative methods for nonlinear equations in this paper we suggest and analyze a new family of iterative methods for solving nonlinear equations using the system of coupled equations coupled with decomposition technique several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

new iterative schemes for nonlinear equations in this paper we suggest and analyze a new iterative method for solving nonlinear equations by using a new decomposition method we also discuss the convergence criteria of these iterative methods several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

some numerical methods for solving nonlinear equations by using decomposition technique in this paper we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations these new methods include the halley method and its variant forms as special cases various numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

new iterative methods for solving nonlinear equation by using homotopy perturbation method in this paper we suggest and analyze a new class of iterative methods for solving nonlinear equations by using the homotopy perturbation method convergence of their method is also considered here we also discuss the efficiency index and computational order of convergence of new methods several numerical examples are given to illustrate the efficiency and performance of these new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

new iterative methods for nonlinear equations by modified hpm a numerical method based on modified homotopy perturbation method hpm is proposed for solving nonlinear algebric equations it is shown that the proposed method has third order convergence to assess its validity and accuracy the method is applied to solve several test problems

a fourth order iterative method for solving nonlinear equations the present paper illustrates an iterative numerical method to solve nonlinear equations of the form f x 0 especially those containing the partial and non partial involvement of transcendental terms comparative analysis shows that the present method is faster than newton raphson method hybrid iteration method new hybrid iteration method and others cost is also found to be minimum than these methods the beauty in our method can be seen because of the optimization in important effecting factors i e lesser number of iteration steps lesser number of functional evaluations and lesser value of absolute error in final as well as in individual step as compared to the other methods this work also demonstrates the higher order convergence of the present method as compared to others without going to the computation of second derivative

a third order newton type method for nonlinear equations based on modified homotopy perturbation method in this paper we present a new iterative method for solving nonlinear algebric equations by using modified homotopy perturbation method we also discuss the convergence criteria of the present method to assess its validity and accuracy the method is applied to solve several test problems

three step iterative methods for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

efficient method for solving a system of nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations by using decomposition technique in conjunction with the coupled system of equations we develop new iterative method for solving a system of nonlinear equations which has better efficiency index we prove the fifth order convergence of the proposed method we provide the comparison of efficiency index with some other well known methods for the implementation and performance of the new method we solve the kinematic synthesis problem for steering chandrasekhar integral equation and combustion problem for a temperature of 3000 c and compare the results with some existing methods

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

real and spurious contributions for the shannon renyi and tsallis entropies abstract a two parameter probability distribution is constructed by dilatation or contraction of the escort probability distribution this transformation involves a physical probability distribution p associated with the system under study and an almost arbitrary reference probability distribution p in contrast to the shannon and renyi entropies the tsallis entropy does not decompose as the sum of the physical contribution due to p and the reference or spurious part owing to p for solving this problem a slight modification to the relation between tsallis and renyi entropies must be introduced the procedure in this paper gives rise to a nonconventional one parameter shannon entropy and to two parameter renyi and tsallis entropies associated with p it also contributes to clarify the meaning and role of the escort probabilities set

newton like iterative methods for solving system of non linear equations abstract homotopy perturbation method hpm is applied to construct a new family of newton like iterative methods for solving system of non linear equations comparison of the result obtained by the present method with newton raphson method reveals that the accuracy and fast convergence of the new method

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

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

on modified newton methods for solving a non linear algebraic equations abstract in this paper we present a new modified newton method for solving a non linear algebraic equation by using the well known nedzhibov s method d k r babajee m z dauhoo an analysis of the properties of the variants of newton s method with third order convergence applied mathematics and computation 183 1 2006 659 684 we proposed a new iteration method and we show by one equation that this new iteration method is more quickly convergence than newton s method

fifth order iterative methods for solving nonlinear equations abstract in this paper we suggest and analyze a new two step iterative method for solving nonlinear equation f x 0 by rewriting the given nonlinear equation as a coupled system of equations and using the taylor series it is shown that this new iterative method is of fifth order several examples are given to illustrate its performance and efficiency comparison with other methods is also given this method can be viewed as an improvement of the halley s method

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

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

higher order iterative schemes for nonlinear equations using decomposition technique in this paper we suggest and analyze some unique recurrence relations which can generate different classes of iterative methods for solving nonlinear equations using the system of coupled equations together with decomposition technique by using an auxiliary function various numerical examples are given to illustrate the efficiency and performance of the newly suggested methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

on two level optimization decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which have often existed in practice similarly tractable game theoretic approaches have not allowed for a continuous solution space in which one player s decision restricts the feasible choices of another this correspondence offers a formulation to help model this type of decision making hierarchy characterizations and algorithmic approaches for a class of two level problems are discussed

new iterative technique for solving a system of nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations in this paper a new family of iterative methods for solving a system of nonlinear equations is developed by using a new decomposition technique the convergence of the new methods is proved efficiency index of the proposed methods is discussed and compared with some other well known methods the upper bounds of the error and the radius of convergence of the methods are also found for the implementation and performance of the new methods the combustion problem streering problem and van der pol equation are solved and the results are compared with some existing methods several new iterative methods are derived from the general iterative scheme using the ideas and techniques of this paper one may be able to suggest and investigate a wide class of iterative methods for solving the system of nonlinear equations this is another direction of future research

two long standing problems in tsallis statistics abstract on the basis of tsallis entropy and the joint probability factorization condition two controversial problems existing in tsallis statistics are investigated where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so called generalized zeroth law of thermodynamics or not the results obtained show clearly that like entropy energy is also nonextensive in tsallis statistics and that the zeroth law of thermodynamics has been implicitly used in tsallis statistics since 1988 moreover it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in tsallis statistics because its corollary is in contradiction with the zeroth law of thermodynamics

renyi and tsallis entropies for incomplete or overcomplete systems of events abstract in this article shannon renyi and tsallis entropies are considered for a system of events characterized by an arbitrary probability distribution p that can be incomplete complete or overcomplete after a suitable transformation that leads to the escort probabilities of p these can be written as the canonical probability distribution for a set of pseudo energies hartley information e n ln p n and a dimensionless parameter q that plays the role of thermodynamics several relations between the entropies are presented including the analysis of compound systems the method is illustrated with an example

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

he s parameter expanding methods for strongly nonlinear oscillators ji huan he s work on asymptotic techniques is briefly reviewed and his parameter expanding methods including modified lindstedt poincare method and bookkeeping parameter method are discussed in detail some remarkable virtues of the methods are exploited and their applications are illustrated

iterative methods to nonlinear equations homotopy perturbation method is applied to construct a new iterative method for solving nonlinear algebraic equations the convergence of the new scheme is proposed an at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of the new method

a note on the new iteration method for solving algebraic equations in ji huan he a new iteration method for solving algebraic equations appl math comput 135 2003 81 84 a new iteration method for solving algebraic equations has been proposed in this paper we show for one equation which given by the author and some other equations that the new iteration method fails to obtain expected results hence in contrast to previous claims it is no more quickly convergent than newton s method and may in fact be failed

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