non uniform specification and large deviations for weak gibbs measures we establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak gibbs measures under some mild assumptions we obtain upper and lower bounds for the measure of deviation sets of some non uniformly expanding maps including quadratic maps and robust multidimensional non uniformly expanding local diffeomorphisms for that purpose a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non uniformly expanding local diffeomorphisms and viana maps

on the lifetime behavior of a discrete time shock model in this article we study a shock model in which the shocks occur according to a binomial process i e the interarrival times between successive shocks follow a geometric distribution with mean 1 p according to the model the system fails when the time between two consecutive shocks is less than a prespecified level this is the discrete time version of the so called d shock model which has been previously studied for the continuous case we obtain the probability mass function and probability generating function of the system s lifetime we also present an extension of the results to the case where the shock occurrences are dependent in a markovian fashion

δ shock model based on polya process and its optimal replacement policy abstract shock models are of great interest in engineering reliability among the others the shock model has been widely studied in the literature in this model the system breaks down due to the arrivals of two successive shocks which are too close to each other that is the system fails when the time between two consecutive shocks falls below a fixed threshold in the literature the shock model has been mostly studied by assuming that shocks arrive according to a renewal process so that the interarrival times between shocks are independent and identically distributed in the current paper we consider the case when the shock arrival process is described by a polya process which has dependent interarrival times in particular we obtain survival function and mean lifetime of the system and study the optimal replacement policy for the shock model based on polya process

runs in superpositions of renewal processes with applications to discrimination wald and wolfowitz ann math statist 11 1940 147 162 introduced the run test for testing whether two samples of i i d random variables follow the same distribution here a run means a consecutive subsequence of maximal length from only one of the two samples in this paper we contribute to the problem of runs and resulting test procedures for the superposition of independent renewal processes which may be interpreted as arrival processes of customers from two different input channels at the same service station to be more precise let sn n 1 and tn n 1 be the arrival processes for channel 1 and channel 2 respectively and wn n 1 their be superposition with counting process n t def sup n 1 wn t let further rn be the number of runs in w1 wn and rt rn t the number of runs observed up to time t we study the asymptotic behavior of rn and rt first for the case where sn n 1 and tn n 1 have exponentially distributed increments with parameters 1 and 2 and then for the more difficult situation when these increments have an absolutely continuous distribution these results are used to design asymptotic level tests for testing 1 2 against 1 2 in the first case and for testing for equal scale parameters in the second

dimension and product structure of hyperbolic measures we prove that every hyperbolic measure invariant under a c 1 fi difieomorphism of a smooth riemannian manifold possesses asymptotically almost local product structure i e its density can be approximated by the product of the densities on stable and unstable manifolds up to small exponentials this has not been known even for measures supported on locally maximal hyperbolic sets using this property of hyperbolic measures we prove the long standing eckmann ruelle conjecture in dimension theory of smooth dynamical systems the pointwise dimension of every hyperbolic measure invariant under a c 1 fi difieomorphism exists almost everywhere this implies the crucial fact that virtually all the characteristics of dimension type of the measure including the hausdorfi dimension box dimension and information dimension coincide this provides the rigorous mathematical justiflcation of the concept of fractal dimension for hyperbolic measures

assessment of a generalized discrete time mixed δ shock model for the multi state systems abstract in this paper the life behavior of a shock model is studied when the external shocks occur according to a binomial process whose interarrival times between successive shocks follow a geometric distribution the system transits into a lower partially working state upon the occurrence of each interarrival time between two successive shocks less than a critical threshold say the system fails when k out of interarrival times between two successive shocks are less than or the magnitude of the shock is larger than the other critical level say such a model creates a multi state system having a number of different states the probability mass functions of system s life time the time spent by the system in a perfectly functioning state and the total time spent by the system in partially working states are derived for the proposed model the corresponding probability generating functions are also derived the case of markov shock occurrences is also studied to illustrate the model studied in this paper some numerical examples are also considered finally an application in insurance is also provided

divergence points of self similar measures and packing dimension fractals multifractals hausdorff measure packing measure divergence points local dimension normal numbers

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

weak uninorm aggregation operators abstract by weakening the identity condition of uninorm a general class of associative aggregation operators called weak uninorm is introduced it is proved that continuous weak uninorms are the combination of continuous t norm and continuous t conorm through a median operator the representation theorem for archimedean weak uninorm is also given finally the counting number of the identity elements of weak uninorm is also investigated

dense lattices in dimensions 27 29 we exhibit integral lattices which are denser than the laminated lattices in dimensions 27 29

some properties of weak uninorms a weak uninorm is not only a generalization of a uninorm but also of a nullnorm in this paper we will show that if a weak uninorm is archimedean then it is an archimedean nullnorm and if a weak uninorm is e archimedean then it is an archimedean uninorm moreover the de morgan triples of the weak uninorms will be characterized too

different asymptotic behavior versus same dynamical complexity recurrence ir regularity abstract for any dynamical system t x x of a compact metric space x with g almost product property and uniform separation property under the assumptions that the periodic points are dense in x and the periodic measures are dense in the space of invariant measures we distinguish various periodic like recurrences and find that they all carry full topological entropy and so do their gap sets in particular this implies that any two kind of periodic like recurrences are essentially different moreover we coordinate periodic like recurrences with ir regularity and obtain lots of generalized multi fractal analyses for all continuous observable functions these results are suitable for all shifts 1 topological mixing subshifts of finite type topological mixing expanding maps or topological mixing hyperbolic diffeomorphisms etc roughly speaking we combine many different eyes i e observable functions and periodic like recurrences to observe the dynamical complexity and obtain a refined dynamical structure for recurrence theory and multi fractal analysis

localized pressure and equilibrium states we introduce the notion of localized topological pressure for continuous maps on compact metric spaces the localized pressure of a continuous potential varphi is computed by considering only those n epsilon separated sets whose statistical sums with respect to an m dimensional potential phi are close to a given value w in mathbb r m we then establish for several classes of systems and potentials varphi and phi a local version of the variational principle we also construct examples showing that the assumptions in the localized variational principle are fairly sharp next we study localized equilibrium states and show that even in the case of subshifts of finite type and holder continuous potentials there are several new phenomena that do not occur in the theory of classical equilibrium states in particular we construct an example with infinitely many ergodic localized equilibrium states we also show that for systems with strong thermodynamic properties and w in the interior of the rotation set of phi there is at least one and at most finitely many localized equilibrium states

c sets of n uninorms the concept of n uninorms was introduced in our earlier paper which is based on the existence of an n neutral element for an associative monotone non decreasing in both variables and commutative amc binary operator on 0 1 there it was shown that the number of subclasses of n uninorms is the n 1 th catalan number an expression for the arbitrary member of each subclass was also given which is recursive in nature in this paper we introduce a unique ordered set of distinct integers between 0 and n called c sets for each subclass of n uninorms this enables us to 1 obtain an expression for arbitrary member of each subclass which is non recursive in nature 2 identify the minimum and the maximum members in general and of idempotent members in particular in each subclass 3 relate c sets of de morgan pairs for strict negation of n uninorms from different subclasses 4 convert theoretical results into construction procedures which are algorithmic in nature in process we generalize some of the existing results for uninorms in the literature

bounds for the lq spectra of a self similar multifractal not satisfying the open set condition abstract by now the l q spectra of self similar measures satisfying the so called open set condition is well understood however if the open set condition is not satisfied then almost nothing is known in this paper we provide non trivial bounds for the l q spectra of an arbitrary self similar measure we emphasize that we are considering arbitrary self similar measures and sets which are not assumed to satisfy the open set condition or similar separation conditions

the mixed lq spectra of self conformal measures satisfying the weak separation condition abstract by now the l q spectra of self conformal measures satisfying the so called open set condition are well understood however if the open set condition is not satisfied then almost nothing is known in this paper we compute the mixed l q spectra for self conformal measures which have bound distortion property and satisfy the weak separation condition

entropy spectrum of lyapunov exponents for nonhyperbolic step skew products and elliptic cocycles we study the fiber lyapunov exponents of step skew product maps over a complete shift of n n ge2 symbols and with c1 diffeomorphisms of the circle as fiber maps the systems we study are transitive and genuinely nonhyperbolic exhibiting simultaneously ergodic measures with positive negative and zero exponents examples of such systems arise from the projective action of 2 times 2 matrix cocycles and our results apply to an open and dense subset of elliptic mathrm sl 2 mathbb r cocycles we derive a multifractal analysis for the topological entropy of the level sets of lyapunov exponent the results are formulated in terms of legendre fenchel transforms of restricted variational pressures considering hyperbolic ergodic measures only as well as in terms of restricted variational principles of entropies of ergodic measures with a given exponent we show that the entropy of the level sets is a continuous function of the lyapunov exponent the level set of the zero exponent has positive but not maximal topological entropy under the additional assumption of proximality as for example for skew products arising from certain matrix cocycles there exist two unique ergodic measures of maximal entropy one with negative and one with positive fiber lyapunov exponent

multifractal analysis for expanding interval maps with infinitely many branches in this paper we investigate multifractal decompositions based on values of birkhoff averages of functions from a class of symbolically continuous functions this will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches we show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches 1 setting let x d be a metric space and t x x be a piecewise continuous transformation let x r be a real valued function called a potential the birkhoff average of is defined by

specification on the interval we study the consequences of discontinuities on the specification property for interval maps after giving a necessary and sufficient condition for a piecewise monotonic piecewise continuous map to have this property we show that for a large and natural class of families of such maps including the 3 transformations the set of parameters for which the specification property holds though dense has zero lebesgue measure thus regarding the specification property the general case is at the opposite of the continuous case solved by a m blokh russian math surveys 38 1983 133 134 for which we give a proof

multifractal analysis of lyapunov exponent for continued fraction and manneville pomeau transformations and applications to diophantine approximation we extend some of the theory of multifractal analysis for conformal expanding systems to two new cases the non uniformly hyperbolic example of the manneville pomeau equation and the continued fraction transformation a common point in the analysis is the use of thermodynamic formalism for transformations with infinitely many branches

multifractal analysis of asymptotically additive sequences for saturated maps we effect a complete multifractal analysis of the dimension spectra obtained from asymptotically additive sequences of continuous functions this includes for example the class of maps with the specification property we consider also the more general cases of ratios of sequences and of multidimensional spectra in which a single sequence is replaced by a vector of sequences in addition we establish a conditional variational principle for the topological pressure of a continuous function on the level sets of an asymptotically additive sequence again in the former general setting finally we apply our results to the dimension spectra of an average conformal repeller in particular we obtain almost automatically a conditional variational principle for the hausdorff dimension of the level sets obtained from an asymptotically additive sequence

topological entropy on points without physical like behaviour for c 1 transitive anosov diffeomorphisms we consider the sets of irregular points without physical like behaviour and regular points without physical like behaviour respectively and show that they all carry full topological entropy roughly speaking physical like measures do not affect the dynamical complexity of the regular set and the irregular set in the sense of topological entropy

relation between neutral element and annihilator in absorption equation abstract the absorption identities in algebra give a relationship between two associative and commutative binary operators join and meet we generalize these operators into a new class of binary operators and study their structures in the context of absorption equation and show that the study of absorption equation involving triangular norms triangular conorms uninorms and nullnorms in the literature are special cases of our study

structure of n uninorms in this paper we study binary operators on 0 1 which are associative monotone non decreasing in both variables and commutative amc with neutral element in this work we generalize the concept of neutral element and this generalization gives rise to a new class of amc binary operators on 0 1 called n uninorms n uninorms are denoted as u n where n comes from the generalization of the neutral element we study the structure of n uninorms the structure resembles an ordinal sum structure made up of n uninorms we characterize some special cases of them based on some continuity considerations and show that t norms t conorms uninorms and nullnorms t operators are special cases of n uninorms we also show that given n there are n 1 classes of operators in u n and each of them has many subclasses we also study the frank equation involving n uninorms and show that we need to consider only n uninorms for the study finally we show that the total number of subclasses of operators in u n follows the famous series called catalan numbers

mixed generalized dimensions of self similar measures abstract classical multifractal analysis studies the local scaling behaviour of a single measure however recently mixed multifractal has generated interest mixed multifractal analysis studies the simultaneous scaling behaviour of finitely many measures and provides the basis for a significantly better understanding of the local geometry of fractal measures the purpose of this paper is twofold firstly we define and develop a general and unifying mixed multifractal theory of mixed renyi dimensions also sometimes called the generalized dimensions mixed l q dimensions and mixed coarse multifractal spectra for arbitrary doubling measures secondly as an application of the general theory developed in this paper we provide a complete description of the mixed multifractal theory of finitely many self similar measures

entropy preservation under markov coding using the notion of topological entropy for non compact sets we prove that for a c1 map with a finite markov partition the corresponding coding map preserves topological entropy of subsets we also provide an example of a piecewise linear conformal repeller with a markov coding decreasing topological entropy these results are generalized to the notions of u dimensions

q geometric and q binomial distributions of order k abstract in this paper we generalize geometric and binomial distributions of order k to q geometric and q binomial distributions of order k using bernoulli trials with a geometrically varying success probability in particular we derive expressions for the probability mass functions of these distributions for q 1 these distributions reduce to geometric and binomial distributions of order k which have been extensively studied in the literature

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above

on the mean and extreme distances between failures in markovian binary sequences this paper is concerned with the mean minimum and maximum distances between two successive failures in a binary sequence consisting of markov dependent elements these random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented

nature of weak generalized synchronization in chaotically driven maps weak generalized synchrony in a drive response system occurs when the response dynamics is a unique but nondifferentiable function of the drive in a manner that is similar to the formation of strange nonchaotic attractors in quasiperiodically driven dynamical systems we consider a chaotically driven monotone map and examine the geometry of the limit set formed in the regime of weak generalized synchronization the fractal dimension of the set of zeros is studied both analytically and numerically we further examine the stable and unstable sets formed and measure the regularity of the coupling function the stability index as well as the dimension spectrum of the equilibrium measure can be computed analytically

entropy of c 1 diffeomorphisms without a dominated splitting a classical construction due to newhouse creates horseshoes from hyperbolic periodic orbits with large period and weak domination through local c 1 perturbations our main theorem shows that when one works in the c 1 topology the entropy of such horseshoes can be made arbitrarily close to an upper bound deriving from ruelle s inequality i e the sum of the positive lyapunov exponents or the same for the inverse diffeomorphism whichever is smaller adapting classical techniques we use perturbations that are local and can be chosen to preserve volume or symplectic form or a homoclinic connection this optimal entropy creation yields a number of consequences for c 1 generic diffeomorphisms especially in the absence of a dominated splitting for instance in the conservative settings we find formulas for the topological entropy deduce that the topological entropy is continuous but not locally constant at the generic diffeomorphism and we prove that these generic diffeomorphisms have no measure of maximum entropy in the dissipative setting we show the locally generic existence of infinitely many homoclinic classes with entropy bounded away from zero