the periodic boundary value problem for semilinear elastic beam equations the resonance case this paper discusses the existence of generalized solutions to periodic boundary value problems for semilinear elastic beam equations under a resonance condition the argument presented makes use of the global inverse theorem and galerkin s method

the sample average approximation method for stochastic discrete optimization in this paper we study a monte carlo simulation based approach to stochastic discrete optimization problems the basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function the obtained sample average optimization problem is solved and the procedure is repeated several times until a stopping criterion is satisfied we discuss convergence rates stopping rules and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem

remarks on the behavior of the ising chain in the generalized statistics abstract the behavior of the ising chain within tsallis generalization of the boltzmann gibbs statistics is reanalyzed taking into account a recently proposed connection between this theory and a generalized thermodynamics

distributionally robust convex optimization distributionally robust optimization is a paradigm for decision making under uncertainty where the uncertain problem data are governed by a probability distribution that is itself subject to uncertainty the distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker s prior information in this paper we propose a unifying framework for modeling and solving distributionally robust optimization problems we introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold these ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases they also allow us to characterize distributional families in terms of several classical and or robust statistical indicators that have not yet been studied in the context of robust optimization we determine conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable we also provide tractable conservative approximations for problems that violate these conditions

dynamical aspects of tsallis entropy abstract the description of the temporal evolution of some physical systems is tackled from an information theory view point in which tsallis entropy is extremalized with the constraints posed by the knowledge of the generalized expectation values of a selected set of observables the concomitant tsallis density operator is shown to be a particular solution of von neumann s equation and tsallis entropy is seen to provide one with a constant of the motion the pertinent ideas are illustrated with reference to the larmor precession

provably near optimal sampling based policies for stochastic inventory control models in this paper we consider two fundamental inventory models the single period newsvendor problem and its multiperiod extension but under the assumption that the explicit demand distributions are not known and that the only information available is a set of independent samples drawn from the true distributions under the assumption that the demand distributions are given explicitly these models are well studied and relatively straightforward to solve however in most real life scenarios the true demand distributions are not available or they are too complex to work with thus a sampling driven algorithmic framework is very attractive both in practice and in theory we shall describe how to compute sampling based policies that is policies that are computed based only on observed samples of the demands without any access to or assumptions on the true demand distributions moreover we establish bounds on the number of samples required to guarantee that with high probability the expected cost of the sampling based policies is arbitrarily close i e with arbitrarily small relative error compared to the expected cost of the optimal policies which have full access to the demand distributions the bounds that we develop are general easy to compute and do not depend at all on the specific demand distributions

asymptotic bifurcation results for coupled nonlinear wave equations with variable coefficients abstract this paper is concerned with the bifurcation phenomenon of large amplitude periodic solutions of coupled nonlinear wave equations with either constant or variable coefficients such model arises when two waves propagate simultaneously in nonisotropic media the change of degree argument is used to obtain necessary and sufficient conditions for the existence of asymptotic bifurcation points with respect to the matrix spectrum the results we get are also valid for uncoupled systems by changing one of our assumptions on the nonlinear term we also obtain the necessary and sufficient conditions for the existence of the standard bifurcation points

the data driven newsvendor problem new bounds and insights consider the newsvendor model but under the assumption that the underlying demand distribution is not known as part of the input instead the only information available is a random independent sample drawn from the demand distribution this paper analyzes the sample average approximation saa approach for the data driven newsvendor problem we obtain a new analytical bound on the probability that the relative regret of the saa solution exceeds a threshold this bound is significantly tighter than existing bounds and it matches the empirical accuracy of the saa solution observed in extensive computational experiments this bound reveals that the demand distribution s weighted mean spread affects the accuracy of the saa heuristic

generalized hausdorff inverse moment problem abstract we consider a generalization of hausdorff moment problem in which the inputs are generalized moments defined by n 0 1 x n f x d x n 1 2 where is a real number and f x is the probability density function to be determined the necessary and sufficient conditions for the existence of the solution are established the convergence of the sequence of solutions for the corresponding finite problem when the number of input moments increases is also studied we show how to construct this sequence by using a maximum entropy principle which is based on tsallis s family of entropies the method is illustrated with a number of examples

generalization of the maier saupe theory of the nematics within tsallis thermostatistics abstract in this study one of the mean field theories in nematics the maier saupe theory mst is generalized within tsallis thermostatistics tt the variation of the order parameter versus temperature has been investigated and compared with experimental data for p azoxyanisole paa so far we believe that this is the first attempt at the application of tt in liquid crystals it is well known that mst fails to explain the experimental data for some of the nematics one of which is paa however generalized mst is able to account for the experimental data for a long range of temperatures also in this study the effect of nonextensivity is shown for various values of the entropic index

a semiclassical statistical model for quantum dissipation abstract the dynamical problem posed by the coupling of quantal to classical degrees of freedom is tackled within the framework of the quantum friction phenomenon by recourse to statistical methods embedded within jaynes maximum entropy principle

stochastic programming approach to optimization under uncertainty in this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems we argue that two stage say linear stochastic programming problems can be solved with a reasonable accuracy by monte carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages we discuss an extension of coherent risk measures to a multistage setting and in particular dynamic programming equations for such problems

human brain dynamics the analysis of eeg signals with tsallis information measure we undertake the study of human eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario dierent information measures are employed it is shown that non extensive ones seem to be of particular usefulness their use opens up perspectives of building up automatic detection devices conjectures concerning general characteristics of focal epilepsy are formulated on the basis of a tsallis type of analysis c 1999 elsevier science b v all rights reserved

bifurcation problems for the laplacian in ⁿ in this paper we consider the bifurcation problem div ivulp 2vu ag x julp 2u f a x u in rn with p 1 we show that a continuum of positive solutions bifurcates out from the principal eigenvalue a1 of the problem div ivuip 2vu ag x ulp 2u here both functions f and g may change sign

the classical n body problem within a generalized statistical mechanics the modifications that must be introduced within the framework of standard classical n body statistical mechanics techniques in order to deal with the recently proposed generalized scenario of non extensive statistical mechanics are discussed a generalized version of the equipartition theorem is shown to hold the ideal gas is revisited as a simple application

an adaptive distribution free algorithm for the newsvendor problem with censored demands with applications to inventory and distribution we consider the problem of optimizing inventories for problems where the demand distribution is unknown and where it does not necessarily follow a standard form such as the normal we address problems where the process of deciding the inventory and then realizing the demand occurs repeatedly the only information we use is the amount of inventory left over rather than attempting to estimate the demand distribution we directly estimate the value function using a technique called the concave adaptive value estimation cave algorithm cave constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain since it is a sampling based method cave does not require knowledge of the underlying sample distribution the result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi gradient methods and more flexible than analytical techniques that require distribution information in addition we demonstrate near optimal behavior of the cave approximation in experiments involving two different types of stochastic programs the newsvendor stochastic inventory problem and two stage distribution problems

resonance in nonlinear wave equations with x dependent coefficients abstract this paper is devoted to the existence results for the one dimensional wave equation with x dependent coefficients when resonance occurs at the eigenvalue r n by using the topological degree theory the authors get a result which is similar to that in the literature

generalized entropy as a measure of quantum uncertainty abstract a generalized entropy is used in order to advance a different form of expressing the uncertainty principle of quantum mechanics we consider the generalized entropic formulation for different pairs of incompatible observables in particular we study the number phase entropic uncertainty measure for the case of coherent states within the pegg barnett theory we also tackle the situation of operators with continuous spectra where a correlation functional is calculated in terms of generalized joint and marginal entropies for harmonic oscillator wavefunctions

study of the mean field renormalization group method with the tsallis statistics abstract the phase transition of the ising model in d dimensional lattice is reanalyzed by using the mean field renormalization group method within the tsallis generalization of the boltzmann gibbs statistics bgs the critical temperature t c is obtained explicitly for a general dimension d and a factor q present in the generalized statistics for clusters of one n 1 and two n 2 spind in the q 1 limit the present work reduces to the results of indekeu et al j phys a 15 1982 l291 with the usual bgs for a linear chain d 1 the system presents a phase transition for q 1 when we have q 1 t c d q is proportional to the factor q in accordance with the result of mean field approximation

existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system abstract in this paper the existence of positive doubly periodic solutions for nonlinear telegraph system is discussed using the method of upper and lower solutions

generalization of the single site callen identity within tsallis statistics abstract within the framework of a generalized thermostatistics introduced by tsallis we establish the generalization of the single site callen identity it is used to calculate the critical temperature of the ising ferromagnet within a consistently generalized mean field approximation

the fluctuation dissipation theorem in the framework of the tsallis statistics in the framework of a generalized statistical mechanics introduced recently by tsallis 1993 we derive a generalized form of the fluctuation dissipation theorem which expresses a relation between extended susceptibilities and equilibrium fluctuations to achieve this we consistently propose a generalized functional form for the instantaneous distribution function the present theorem recovers as particular cases the corresponding generalized relations already obtained for the specific heat in terms of the generalized energy fluctuations and for the susceptibility of a magnetic system under the action of a uniform magnetic field

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

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

generalized distribution functions and an alternative approach to generalized planck radiation law abstract in this study recently introduced generalized distribution functions are summarized and by using one of these distribution functions namely generalized planck distribution an alternative approach to the generalized planck law for the blackbody radiation has been tackled the expression obtained is compared with the expression given by c tsallis et al phys rev e 52 1995 1447 and it is found that this approximate scheme provides bounds to the exact result depending on the values of q index

global results concerning bifurcation for fredholm maps of index zero with a transversality condition on considere l equation f x ax bx r x 0 ou a b est la derivee de frechet de f a l origine dans x et r un terme d ordre eleve x est un espace de banach et f x r y est un operateur non lineaire continu et y un espace de banach on etudie comment l ensemble solution varie avec le parametre reel

a generalized class of certainty and information measures abstract unlike the usual definition of measures of information in terms of the relation between information and uncertainty a different approach is followed in this paper in which the relation between certainty and information plays a central role information measures are introduced with the help of certainty measures within this framework this approach leads to three generalized classes of information measures and unifies the known measures of information into one generalized probabilistic theory of discrete information measures

irreversible thermodynamics in the framework of tsallis entropy abstract the symmetry of the kinetic onsager coefficients is proved in the context of tsallis generalization of boltzmann gibbs statistics a generalized nyquist theorem is also introduced the analysis of the noise spectrum of the thermodynamics fluctuation is presented in the framework of tsallis entropy a comment about the spectrum 1 in connection with non gaussian statistics is also discussed

on the bifurcation of large amplitude solutions for a system of wave and beam equations we consider the existence of solutions for linearly coupled system of wave and beam equation with a sublinear perturbation the main concept is the matrix spectrum which is a natural extension of the usual spectrum using the standard change of degree argument we shall find necessary and sufficient conditions for the existence of asymptotic bifurcation with respect to the matrix spectrum both in one parameter and four parameter cases obviously the results can be modified for more general systems of partial differential equations

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

ising chain in the generalized boltzmann gibbs statistics abstract the partition function and specific heat of the ising chain are evaluated in a generalization of the boltzmann gibbs statistics the extensivity and the influence of the ground state energy in the thermodynamical properties are discussed

schaefer type theorem and periodic solutions of evolution equations abstract two fixed point theorems for the sum of contractive and compact operators are obtained in this paper which generalize and improve the corresponding results in h schaefer uber die methode der a priori schranken math ann 129 1955 415 416 t a burton integral equations implicit functions and fixed points proc amer math soc 124 1996 2383 2390 v i istr tescu fixed point theory an introduction reidel dordrecht 1981 t a burton k colleen a fixed point theorem of krasnoselskii schaefer type math nachr 189 1998 23 31 d r smart fixed point theorems cambridge univ press cambridge 1980 as the applications for the results we obtain the existence of periodic solutions for some evolution equations with delay which extend the corresponding results in t a burton b zhang periodic solutions of abstract differential equations with infinite delay j differential equations 90 1991 357 396

regret in the newsvendor model with partial information traditional stochastic inventory models assume full knowledge of the demand probability distribution however in practice it is often difficult to completely characterize the demand distribution especially in fast changing markets in this paper we study the newsvendor problem with partial information about the demand distribution e g mean variance symmetry unimodality in particular we derive the order quantities that minimize the newsvendor s maximum regret of not acting optimally most of our solutions are tractable which makes them attractive for practical application our analysis also generates insights into the choice of the demand distribution as an input to the newsvendor model in particular the distributions that maximize the entropy perform well under the regret criterion our approach can be extended to a variety of problems that require a robust but not conservative solution

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

profit estimation error in the newsvendor model under a parametric demand distribution we consider the newsvendor model in which uncertain demand is assumed to follow a probabilistic distribution with known functional form but unknown parameters these parameters are estimated unbia

nonnegative doubly periodic solutions for nonlinear telegraph system with twin parameters in this paper by using krasnosel skii fixed point theorem and under suitable conditions we present the existence and multiplicity of nonnegative doubly periodic solutions for the following system u t t u x x c 1u t a 1 1 t x u a 1 2 t x v b 1 t x f t x u v v t t v x x c 2v t a 2 1 t x u a 2 2 t x v b 2 t x g t x u v where c i 0 is a constant a 1 1 t x a 2 2 t x b 1 t x b 2 t x c r 2 r a 1 2 t x a 2 1 t x c r 2 r f t x u v g t x u v c r 2xr xr r and a i j b i f g are email protected in t and x we derive two explicit intervals of b 1 t x and b 2 t x such that for any b 1 t x and b 2 t x in the two intervals respectively the existence of at least one solution for the system is guaranteed and the existence of at least two solutions for b 1 t x and b 2 t x in appropriate intervals is also discussed

irreversible processes the generalized affinities within tsallis statistics abstract within the generalized statistical mechanics introduced recently by tsallis the generalized form of the affinities the quantities which drive a process in the theory of irreversible thermodynamics was derived the affinities were obtained by considering changes in the generalized entropy s q aub of a system composed by two subsystems a and b the non extensive character of the tsallis entropy is taken into account at the end the equilibrium condition is discussed and the zeroth law in the framework of the generalized thermodynamics is consistently recovered as in the usual case two systems which are in equilibrium with a third one are necessarily in equilibrium among them and share the same temperature

an efficient monte carlo algorithm for overcoming broken ergodicity in the simulation of spin systems abstract a new monte carlo algorithm which provides enhanced sampling in the calculation of equilibrium thermodynamic properties of spin systems is presented the algorithm proposed performs trial moves based on the generalized statistical distributions derived from a modification of the gibbs shannon entropy by tsallis results for a two dimensional ising model demonstrate that the algorithm leads to a greatly enhanced rate of barrier crossing and convergence in the calculation of equilibrium thermodynamic averages comparison is made with standard metropolis monte carlo

robust sample average approximation sample average approximation saa is a widely popular approach to data driven decision making under uncertainty under mild assumptions saa is both tractable and enjoys strong asymptotic performance guarantees similar guarantees however do not typically hold in finite samples in this paper we propose a modification of saa which we term robust saa which retains saa s tractability and asymptotic properties and additionally enjoys strong finite sample performance guarantees the key to our method is linking saa distributionally robust optimization and hypothesis testing of goodness of fit beyond robust saa this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data driven procedures that are based upon distributionally robust optimization this analysis provides insight into the practical performance of these various methods in real applications we present examples from inventory management and portfolio allocation and demonstrate numerically that our approach outperforms other data driven approaches in these applications

nonnegative doubly periodic solutions for nonlinear telegraph system abstract this paper deals with the nonnegative doubly periodic solutions for nonlinear telegraph system u t t u x x c 1 u t a 11 t x u a 12 t x v b 1 t x f t x u v v t t v x x c 2 v t a 21 t x u a 22 t x v b 2 t x g t x u v where c i 0 is a constant a 11 a 22 b 1 b 2 c r 2 r a 12 a 21 c r 2 r f g c r 2 r r r and a i j b i f g are 2 periodic in t and x we show the existence and multiplicity results when 0 a i i t x c i 2 4 and f g are superlinear or sublinear on u v by using the fixed point theorem in cones

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 treatment of autonomous systems with divergencelless flows abstract statistical mechanics sm has been quite successful in providing one with exact or at least approximate descriptions of the time dependent solutions of the liouville or of the von neumann equation within the context of hamiltonian dynamics hd here we investigate how to extend some of its ideas to more general dynamical systems we find that for systems that retain from hd just the divergenceless character of the phase space flow many ideas borrowed from the maximum entropy principle approach to sm apply in such a generalized context as well

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

a nonparametric asymptotic analysis of inventory planning with censored demand we study stochastic inventory planning with lost sales and instantaneous replenishment where contrary to the classical inventory theory knowledge of the demand distribution is not available furthermore we observe only the sales quantity in each period and lost sales are unobservable that is demand data are censored the manager must make an ordering decision in each period based only on historical sales data excess inventory is either perishable or carried over to the next period in this setting we propose nonparametric adaptive policies that generate ordering decisions over time we show that the t period average expected cost of our policy differs from the benchmark newsvendor cost the minimum expected cost that would have incurred if the manager had known the underlying demand distribution by at most o 1 t0 5