on the existence of a limit value in some nonexpansive optimal control problems we investigate the limit of the average value of an optimal control problem when the horizon converges to infinity for this aim we suppose suitable nonexpansive like assumptions which does not imply that the limit is independent of the initial state as is usually done in the literature

new series expansion data for surface and bulk resistivity and conductivity in two dimensional percolation low density series expansions are obtained for random resistor networks the expansions are obtained on the square lattice to order 18 and on the triangular lattice to order 14 bulk and surface expansions are given for both resistive and conductive susceptibilities the balance of the evidence obtained from analysing these series is in favour of the value for the critical exponent of the resistance scale and supports the existence of only a single such scale for bulk and surface susceptibilities this value is in agreement with earlier monte carlo work

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

the fractal dimension and other percolation exponents in four and five dimensions for percolation the fractal dimension df which is identical to the magnetic field scaling power yh has never been calculated for hypercubic lattices of dimension d 5 percolation is studied for systems of high dimensionality using the method of large cell monte carlo position space renormalisation group the estimate df yh 3 69 or 0 02 d 5 and 3 12 or 0 02 d 4 is obtained the thermal scaling power yt 1 nu where nu is the correlation length exponent is calculated yt 1 nu 0 51 or 0 05 d 5 and nu 0 64 or 0 02 d 4 the results are compared with the epsilon expansions of df and nu

a regular model for cluster numbers and structure just below percolation threshold a two dimensional deterministic fractal model is proposed to imitate the geometric texture just below percolation threshold the model is constructed for bond percolation via a rule of bond occupation on the square lattice it show the typical percolation behaviour as a function of a parameter p p is the bond concentration the model describes the approach towards the threshold below criticality the critical bond concentration pc and the correlation length exponent nu are found the scaling property of the cluster size distribution is studied below the threshold the critical concentration and critical exponents are shown to agree with those derived from the regular model proposed for the geometric texture above the threshold the scaling relations for the critical exponents are shown to be satisfied

a regular model for bond percolation the approach towards the threshold a two dimensional regular model is constructed for bond percolation via a rule of bond deletions on the square lattice the model describes the approach towards the threshold the critical bond concentration pc and the correlation length exponent nu are found the fractal geometry of the infinite percolating network and the scaling property of the cluster size distribution are studied above the threshold the infinite percolating network is shown to be reconstructed by the mandelbrot koch curve proposed as the non random model for the infinite cluster at criticality

oscillatory critical amplitudes in hierarchical models we study the oscillatory critical amplitudes of theq states potts model on a diamond hierarchical lattice we consider an example of the generic case finite critical index as well as the degenerate case essential singularity in both cases we compare the magnitude of the oscillations with geometrical characteristics of the julia set of zeroes of the partition function

iterated networks and the spectra of renormalizable electromechanical systems beginning with anlrc network with impedance functionz a sequence of iterated networksnk with impedance functionsz k k 1 2 3 is introduced the asymptotic comportment ofz k and the spectra ofnk are analyzed in terms of the julia set ofz an example is given of an iterated network associated with a cascade of period doubling bifurcations

the fractal dimension of the minimum path in two and three dimensional percolation the authors calculate the fractal dimension d min of the shortest path l between two points on a percolation cluster where l approximately rd min and r is the pythagorean distance between the points they find d min 1 130 or 0 002 for d 2 and 1 34 or 0 01 for d 3

percolation in cluster cluster aggregation processes numerical simulations of diffusion limited and reaction limited cluster cluster aggregation processes of identical particles are performed in a two dimensional box it is shown that for concentrations larger than a characteristic gel concentration the morphology of the resulting spanning cluster at the gel time t g exhibits a crossover length l c between percolation l l c and aggregation l c p the long range correlations are similar to that of percolation the vanishing links in the structure suggest that an homogeneous regime appears at small scales

position space renormalisation group approach to fractal dimensions of an infinite cluster its backbone and cutting bonds for percolation a position space renormalisation group method is presented to study the cluster structure of an infinite cluster at the percolation threshold fractal dimensions of an infinite cluster its backbone and cutting bonds are determined by the small cell method for two dimensional bond percolation it is shown that the fractal dimension of its cutting bonds agrees with the inverse of the connectedness length exponent at the fixed point

orthogonal and l q extremal polynomials on inverse images of polynomial mappings abstract let t be a polynomial of degree n and let k be a compact set with c first it is shown if zero is a best approximation to f from p n on k with respect to the lq norm q 1 then zero is also a best approximation to f t on t 1 k with respect to the l q t norm where t arises from by the transformation t in particular t is the equilibrium measure on t 1 k if is the equilibrium measure on k for q i e the sup norm a corresponding result is presented in this way polynomials minimal on several intervals on lemniscates on equipotential lines of compact sets etc are obtained special attention is given to lq minimal polynomials on julia sets next based on asymptotic results of widom we show that the minimum deviation of polynomials orthogonal with respect to a positive measure on t 1 k behaves asymptotically periodic and that the orthogonal polynomials have an asymptotically periodic behaviour too some open problems are also given

condensed julia sets with an application to a fractal lattice model hamiltonian on considere l ensemble de julia pour l application rationnelle complexe z z 2 e z ou et e sont des parametres complexes dans la limite e 0

red bond exponents of the critical and the tricritical ising model in three dimensions using the wolff and geometric cluster algorithms and finite size scaling analysis we investigate the critical ising and the tricritical blume capel models with nearest neighbor interactions on the simple cubic lattice the sampling procedure involves the decomposition of the ising configuration into geometric clusters each of which consists of a set of nearest neighboring spins of the same sign connected with bond probability p these clusters include the well known kasteleyn fortuin clusters as a special case for p 1 exp 2k where k is the ising spin spin coupling along the critical line k kc the size distribution of geometric clusters is investigated as a function of p we observe that unlike in the case of two dimensional tricriticality the percolation threshold in both models lies at pc 1 exp 2kc further we determine the corresponding red bond exponents as yr 0 757 2 and 0 501 5 for the critical ising and the tricritical blume capel models respectively on this basis we conjecture yr 1 2 for the latter model

systematic density expansion for random resistor networks the authors present a systematic density expansion for calculating transport properties return probabilities and spectral densities for lattice hopping models with diluted randomness the method is applied to a disordered square lattice where the bonds carry conductances sigma 1 and sigma 2 in concentrations c and 1 c respectively and they calculate explicitly the o c and o c2 contributions to the static conductivity diffusion coefficient and to the coefficient beta c of the long time tail in the velocity autocorrelation function vacf upsilon x 0 upsilon x t approximately beta c t 2 to o c the vacf is calculated for all times and shows negative correlation cage effect for all times

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

on the relation of kinetic gelation and percolation we analyse the results of kinetic gelation and propose a diagram compatible with the existing data we introduce the concept of limited and full universality the former refers to systems with an identical subset of critical exponents the latter refers to systems with an identical set of critical exponents the evidence suggests that kinetic gelation and random percolation are in the same limited universality class it appears that the concentration of initiators plays the role of an active parameter similar to that of the interplane coupling in quasi two dimensional king models

the complex potential generated by the maximal measure for a family of rational maps the exact complex potential generated by the maximal measure for a family of rational maps is given the results are of analytical nature because the complex potential does not change nicely if the coordinates of a rational map are changed there exist applications of this result to the theory of moments

a new percolation statistic with unusual properties in bond percolation on lattice with p pc there are unoccupied bonds which if occupied would immediately join the backbone in general when such a bond is occupied several tag end bonds may join the backbone as well the author defines ni to be the number of bonds that would join the backbone if such a bond i were occupied and n to be the average of ni taken over all such bonds on the lattice the author derives a formula for n and finds that for all lattices near pc n gamma bpc p pc 1 where gamma b is the exponent for the divergence of the backbone fraction identical formulae apply to site percolation

graph partitioning induced phase transitions we study the percolation properties of graph partitioning on random regular graphs with n vertices of degree k optimal graph partitioning is directly related to optimal attack and immunization of complex networks we find that for any partitioning process even if nonoptimal that partitions the graph into essentially equal sized connected components clusters the system undergoes a percolation phase

eden growth on fractal media abstract simulations are presented for two dimensional eden growth into fractal networks we find that the fractal dimension of the eden cluster d e does not have a simple behavior when the cluster grows into the structure of a fractal network we also find that d e depends strongly on the minimal path between two arbitrary points in the network backbone and on the number of paths that appear between these two points at each scale

image and video encryption using scan patterns abstract this paper presents a new method for image and video encryption and a first stage lossy video compression based on frames difference before the encryption the encryption methods are based on the scan methodology which is a formal language based two dimensional spatial accessing methodology which can generate very large number of scanning paths or space filling curves the image encryption is performed by scan based permutation of pixels and a substitution rule which together form an iterated product cipher the video encryption is performed by first lossy compressing adjacent frame differences and then encrypting the compressed frame differences the main characteristics of the proposed methods are image encryption first stage compression based frames differences and encryption of video whose compression error can be bounded pixelwise by a user specified value very large number of encryption keys and ability to encrypt large blocks of any digital data results from the use of the methods proposed here are also provided

ac response near percolation threshold transfer matrix calculation in 2d the complex admittivity of a network of resistors and capacitors is calculated at pc on a square lattice using a transfer matrix the loss tangent shows a region of anomalous frequency scaling with t s finite size scaling reveals two crossover frequencies as expected from duality

geometrical properties of swendsen wang clusters abstract several geometrical properties of swendsen wang clusters are studied numerically for the 2d ising and 3 state potts models at the critical temperature the fractal dimensions of the total mass backbone elastic backbone shortest path and red bonds are determined the results agree with some theoretical predictions

almost periodic jacobi matrices associated with julia sets for polynomials let be the jacobi matrix associated with polynomialt z of degreen 2 the spectrum of is the julia set associated witht z which in many cases is a cantor set let 1 denote the result of omitting the first row and column ofj then it is shown that the spectrum of 1 may be purely discrete

iterated function systems and the global construction of fractals iterated function systems i f ss are introduced as a unified way of generating a broad class of fractals these fractals are often attractors for i f ss and occur as the supports of probability measures associated with functional equations the existence of certain p balanced measures for i f ss is established and these measures are uniquely characterized for hyperbolic i f ss the hausdorff besicovitch dimension for some attrac tors of hyperbolic i f ss is estimated with the aid of p balanced measures what appears to be the broadest framework for the exactly computable moment theory of p balanced measures that of linear i f ss and of probabilistic mixtures of iterated riemann surfaces is presented this extensively generalizes earlier work on orthogonal polynomials on julia sets an example is given of fractal reconstruction with the use of linear i f ss and moment theory

resistance and fluctuation of a fractal network of random resistors a non linear law of large numbers the authors study rigorously the resistance and fluctuation of resistance of a large deterministic fractal lattice in the limit of an infinite number of resistors they give estimates on corrections to the effective medium approximation of the total resistance they prove scaling laws for the relative fluctuation and prove that the normalised relative fluctuation converges in distribution to the standard normal variable this is a kind of non linear law of large numbers

backbone exponents of the two dimensional q state potts model a monte carlo investigation we determine the backbone exponent x b of several critical and tricritical q state potts models in two dimensions the critical systems include the bond percolation the ising the q 2 sqrt 3 3 and 4 state potts and the baxter wu model and the tricritical ones include the q 1 potts model and the blume capel model for this purpose we formulate several efficient monte carlo methods and sample the probability p2 of a pair of points connected via at least two independent paths finite size scaling analysis of p2 yields x b as 0 3566 2 0 2696 3 0 2105 3 and 0 127 4 for the critical q 2 sqrt 3 1 2 3 and 4 state potts model respectively at tricriticality we obtain x b 0 0520 3 and 0 0753 6 for the q 1 and 2 potts model respectively for the critical q 0 potts model it is derived that x b 3 4 from a scaling argument we find that at tricriticality x b reduces to the magnetic exponent as confirmed by the numerical results

fractal structure of zeros in hierarchical models we consider an ising and aq state potts model on a diamond hierarchical lattice we give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices ofq these zeros are just the julia set corresponding to the renormalization group transformation

meblin transforms associated with julia sets and physical applications we introduce the mellin transform of the balanced invariant measure associated to the julia set generated by a rational transformation we show that its analytic continuation is a meromorphic function the poles of which are on a semi infinite periodic lattice this allows one to have an understanding of the behavior of the measure near a repulsive fixed point trace identities corresponding to the fact that the analytically continued mellin transform vanishes at negative integers are derived for the polynomial case the quadratic map is first analyzed in detail and the analytic properties of the inverse of the green s function are exhibited of interest is the appearance of a dense set of spikes at dyadic points when the julia set is disconnected these results are used to study the residues of the mellin transform a certain number of physically interesting consequences are derived for the spectral dimensionality of quantum mechanical systems the excitation spectrum of which displays unusual oscillations the appearance of complex critical indices for thermodynamical systems is also discussed in the conclusion

geometry and combinatorics of julia sets of real quadratic maps for real a correspondence is made between the julia setb forz z 2 in the hyperbolic case and the set of chains with the aid of cremer s theorem it is shown how a number of features ofb can be understood in terms of chains the structure ofb is determined by certain equivalence classes of chains fixed by orders of visitation of certain real cycles and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of chains the functional equations obeyed by attractive cycles are investigated and their relation to chains is given the first cascade of period doubling bifurcations is described from the point of view of the associated julia sets and chains certain julia sets associated with the feigenbaum function and some theorems of lanford are discussed

a ruelle operator for a real julia set letr be an expanding rational function with a real bounded julia set and let left lg right left x right sum limits ry x frac g left y right left r left y right right 2 be a ruelle operator acting in a space of functions analytic in a neighbourhood of the julia set we obtain explicit expressions for the resolvent function e left x z lambda right left i lambda l right 1 frac 1 z x and in particular for the fredholm determinantd det i l it gives us an equation for calculating the escape rate we relate our results to orthogonal polynomials with respect to the balanced measure ofr two examples are considered

orthogonality properties of iterated polynomial mappings we consider a measure defined on a complex contour and its associated orthogonal polynomials the action of a polynomial transformation on the measure and the transformation laws of the corresponding orthogonal polynomials are given iterating the transformation provides an invariant measure whose support is the julia set corresponding to the polynomial transformation it appears that up to a constant the iterated polynomials generated by the initial mapping form a subset of the invariant set of orthogonal polynomials which fulfill a three term recursion relation an algorithm is given to compute the coefficients of this recursion relation which can be interpreted as a linear extension of the iterative procedure

non linear conductivity of granular superconductors a novel breakdown problem the authors study a percolating network of highly hysteretic josephson junctions in which each junction is modelled as a piecewise ohmic hysteretic device at the percolation threshold the average voltage drop across a network on a large l l grid is assumed to fall to zero as v approximately i ic l eta as the applied current is reduced to the critical current ic l the finite size monte carlo study gives the value eta 2 0 or 0 1 this value is remarkably close to the result eta 2 obtained by a scaling analysis of a continuum version of the model

inverse problems in fractal construction moment method solution abstract the inverse problem for several classes of fractals in one and two dimensions can be profitably solved via the application of the classical theory of moments this new perspective leads to important results on the reconstruction process when only a finite number of moments of the fractal measures are known while discussing the rigorous aspects of the theory we also implement it via efficient numerical algorithms

the perron frobenius theorem for homogeneous monotone functions if a is a nonnegative matrix whose associated directed graph is strongly connected the perron frobenius theorem asserts that a has an eigenvector in the positive cone r n we associate a directed graph to any homogeneous monotone function f r n r n and show that if the graph is strongly connected then f has a nonlinear eigenvector in r n several results in the literature emerge as corollaries our methods show that the perron frobenius theorem is really about the boundedness of invariant subsets in the hilbert projective metric they lead to further existence results and open problems

a transfer matrix approach to random resistor networks introduces a transfer matrix formulation to compute the conductance of random resistor networks the authors apply this method to strips of width up to 40 and use finite size scaling arguments to obtain an estimate for the conductivity critical exponent in two dimensions t 1 28 or 0 03

the shell model a growth model with a tunable fraction of forgotten growth sites the authors introduce and discuss a new model in which the growth sites are driven with a power law ralpha away from the original seed the concept of forgotten growth sites is developed they find that the fraction of forgotten growth sites the order parameter for this problem is zero for alpha below a critical value alpha c 1 and increases sharply for alpha alpha c with a critical exponent beta approximately 2 3 in two dimensions

transfer matrix calculation of the relative noise exponent in a two dimensional percolating network a new method is given for calculating the relative noise exponent describing the size dependence of macroscopic fluctuations due to microscopic resistance noise of a random resistor network at the percolation threshold pc the macroscopic fluctuation is calculated exactly using the transfer matrix idea in a given network the asymptotic exponent b is found by finite size scaling

computing the smallest fixed point of order preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs the problem of computing the smallest fixed point of an order preserving map arises in the study of zero sum positive stochastic games it also arises in static analysis of programs by abstract interpretation in this context the discount rate may be negative we characterize the minimality of a fixed point in terms of the nonlinear spectral radius of a certain semidifferential we apply this characterization to design a policy iteration algorithm which applies to the case of finite state and action spaces the algorithm returns a locally minimal fixed point which turns out to be globally minimal when the discount rate is nonnegative

ac properties of 2d percolation networks a transfer matrix approach the frequency dependent ac properties of 2d random resistor capacitor mixtures are studied through a numerical transfer matrix method the algorithm which generalises to the complex impedances used by herrmann et al 1984 permits a detailed study of the scaling laws obeyed by the complex dielectric constant in the critical regime low frequency and concentration close to the geometrical percolation threshold the duality property of the system is extensively used throughout the analysis quantities of experimental interest such as the loss angle delta and the cole and cole plot of the dielectric constant are also examined both close to and away from the critical point

density expansion of transport properties on 2d site disordered lattices i general theory a systematic kinetic theory is developed for calculating transport properties on 2d lattices with random site impurities in concentration c which can be modelled by hopping models the authors main results are expressions in terms of lattice sums for the static and frequency dependent conductivity and for the velocity autocorrelation function

spectral theorem for convex monotone homogeneous maps and ergodic control we consider convex maps f rn rn that are monotone i e that preserve the product ordering of rn and nonexpansive for the sup norm this includes convex monotone maps that are additively homogeneous i e that commute with the addition of constants we show that the fixed point set of f when it is nonempty is isomorphic to a convex inf subsemilattice of rn whose dimension is at most equal to the number of strongly connected components of a critical graph defined from the tangent affine maps of f this yields in particular an uniqueness result for the bias vector of ergodic control problems this generalizes results obtained previously by lanery romanovsky and schweitzer and federgruen for ergodic control problems with finite state and action spaces which correspond to the special case of piecewise affine maps f we also show that the length of periodic orbits of f is bounded by the cyclicity of its critical graph which implies that the possible orbit lengths of f are exactly the orders of elements of the symmetric group on n letters

series expansion analysis of the backbone properties of two dimensional percolation clusters low density series expansions for the backbone properties of two dimensional bond percolation clusters are derived and analysed expansions for most of the 14 properties considered are new and are obtained to order on the square lattice and order on the triangular lattice earlier series work was confined to three properties of the square lattice and was to order the fractal dimension of the bonds or sites in the backbone is estimated to be and is intermediate between a previously conjectured field theory value and the latest monte carlo results the union intersection and length of the longest self avoiding paths are found to have the same fractal dimension which is close to and consistent with the field theory conjecture for on the other hand the union intersection and length of the shortest paths are found to have different dimensions and in the case of the intersection the triangular and square lattices are found to have sigificantly different dimensions the fractal dimension of the shortest path also appears to be non universal and we find for the square lattice and for the triangular lattice critical amplitude ratios are considered and found to be in agreement with theoretical inequalities

uniqueness of the fixed point of nonexpansive semidifferentiable maps we consider semidifferentiable possibly nonsmooth maps acting on a subset of a banach space that are nonexpansive either in the norm of the space or in the hilbert s or thompson s metric inherited from a convex cone we show that the global uniqueness of the fixed point of the map as well as the geometric convergence of every orbit to this fixed point can be inferred from the semidifferential of the map at this point in particular we show that the geometric convergence rate of the orbits to the fixed point can be bounded in terms of bonsall s non linear spectral radius of the semidifferential we derive similar results concerning the uniqueness of the eigenline and the geometric convergence of the orbits to it in the case of positively homogeneous maps acting on the interior of a cone or of additively homogeneous maps acting on an am space with unit this is motivated in particular by the analysis of dynamic programming operators shapley operators of zero sum stochastic games

moments of balanced measures on julia sets by a theorem of s demko there exists a balanced measure on the julia set of an arbitrary nonlinear rational transformation on the riemann sphere it is proved here that if the transformation admits an attractive or indifferent cycle then there is a point with respect to which all the moments of a balanced measure exist moreover these moments can be calculated exactly an explicit balanced measure is exhibited in an example where the julia set is the whole sphere and for which the moments with respect to any point do not all exist 1 introduction the julia set for a nonlinear rational transformation on the riemann sphere is the closure of the set of all repulsive cycles of the transformation br fa j the location or distribution of the set is of interest in the theory of iterated maps and it may be characterized by an associated invariant measure in this paper we extend previous results by showing that when there is an attractive or indifferent cycle certain moments of such a measure exist and can be calculated exactly from the rational transformation this means for example that when the julia set is contained strictly in the real line all of the orthogonal polynomials on the set can be calculated as can the entries of the corresponding infinite dimensional jacobi matrices the latter are of the type which have recently been shown to furnish model schrodinger equations for crystals with almost periodic potentials bbm this leads us to the following speculation which provides one reason for our interest in the present topic we note first the frequent occurrence in the physical universe of objects steady state systems which are fractals from some point of

possibly exact fractal dimensions from conformal invariance based on an equivalence between the q state potts model and conformally invariant field theories the author speculates that all fractal dimensionalities of two dimensional percolation are given by the formula d 100 x2 48 where x is an integer the same formula should also apply to self avoiding walks and lattice animals this approach is extended to cluster weighted percolation his conjecture seems to agree with previous exact and numerical results except for the backbone exponent and possibly for lattice animals

a novel determination of the percolation exponent u in three dimensions the authors present an accurate determination of the percolation transport exponent u t s t in three dimensions based on a transfer matrix approach to the ac frequency dependent conductivity and a finite size scaling analysis of the numerical data the phase of the complex conductivity the loss angle assumes the universal value delta c pi 2 1 u at low frequency at the percolation threshold as a test of their numerical scheme the two dimensional exact duality result delta c pi 4 i e s t is recovered with a very good accuracy in three dimensions their data are extrapolated to tan delta c 0 54 or 0 03 i e u 0 69 or 0 02 whereas the usually accepted values s v 0 85 or 0 04 t v 2 2 or 0 1 yield u 0 72 or 0 02 this marginal disagreement can be attributed to ill behaved corrections to finite size scaling

phenomenological renormalisation of monte carlo data for percolation the accuracy of a phenomenological renormalisation which is based on monte carlo data is tested by investigating site percolation in a simple cubic lattice the method appears to be very accurate and can yield precise estimates of the quantities of interest with small to moderate lattice sizes the site percolation threshold of the lattice is predicted to be 0 3115 or 0 0005 if nu is the exponent of correlation length the author finds beta nu approximately 0 48 or 0 01 for the exponent of percolation probability and beta b nu approximately 1 1 or 0 03 for the backbone exponent in agreement with most accurate data currently available an analysis of the data at the percolation threshold based on the standard finite size scaling method also supports the results

personalized information encryption using ecg signals with chaotic functions the development of efficient data encryption to ensure high security of information transmission has long been a popular research subject because electrocardiogram ecg signals vary from person to person and can be used as a new tool for biometric recognition this study introduces an individual feature of ecg with chaotic henon and logistic maps for personalized cryptography this study also develops an encryption algorithm based on the chaos theory to generate initial keys for chaotic logistic and henon maps the proposed personalized encryption system uses a convenient handheld device to collect ecg signals from the user high quality randomness in ecg signals results in a widely expanded key space making it an ideal key generator for personalized data encryption the experiments reported in this study demonstrate the use of this approach in encrypting texts and images and applied of the proposed approach to secure communications

on the invariant sets of a family of quadratic maps the julia setb for the mappingz z 2 is considered where is a complex parameter for 2 a new upper bound for the hausdorff dimension is given and the monic polynomials orthogonal with respect to the equilibrium measure onb are introduced a method for calculating all of the polynomials is provided and certain identities which obtain among coefficients of the three term recurrence relations are given a unifying theme is the relationship betweenb and chains which is explored for 1 4 2 and for with 1 4 with the aid of the bottcher equation thenb is shown to be a holder continuous curve for 1 4

block orthogonal systems for symmetric p forms abstract to study polynomials orthogonal with respect to the logarithmic equilibrium measure on the julia set of a nonlinear polynomial p bessis and his coworkers introduced a symmetric bilinear form the symmetric p form it is a non hermitian variant of a genuine inner product the hermitian p form the main reason for doing so was the existence of a three term recurrence relation between the polynomials of successive degree of an orthogonal system however this is only true if the moment matrix of the symmetric p form is strongly regular in this paper we investigate what happens if this condition is not met we distinguish between the case where an orthogonal system still exists and the one where it does not and illustrate them by z z 2 and p z z 2 1 respectively

scaling of cluster mass between two lines in 3d percolation abstract we consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions and model the porous media by bond percolation at the percolation threshold p c we observe that for many geometrical configurations the mass probability distribution presents power law behavior we determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length w the minimal distance between lines r and the angle between the lines the fractal dimensions of the cluster mass are independent of w r and the slope of the power law regime of the cluster mass is unaffected by changes in these three variables however the characteristic mass of the cluster depends upon we propose new scaling functions that reproduce the dependence of the characteristic mass found in the simulations

fourier acceleration of iterative processes in disordered systems technical details are given on how to use fourier acceleration with iterative processes such as relaxation and conjugate gradient methods these methods are often used to solve large linear systems of equations but become hopelessly slow very rapidly as the size of the set of equations to be solved increases fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm the method is explained for the jacobi relaxation and conjugate gradient methods and is applied to two models the random resistor network and the random central force network in the first model acceleration works very well in the second little is gained we discuss reasons for this we also include a discussion of stopping criteria

some problems on current noise in resistor network abstract we report experimental results on the flicker noise in a fractal lattice the exponent b value is found equal to 1 we give preliminary results on the behaviour of a square lattice made up of resistors whose values are distributed with a r probability

topological properties of diffusion limited aggregation and cluster cluster aggregation the detailed topological or connectivity properties of the clusters formed in diffusion limited aggregation dla and cluster cluster aggregation cca are considered for spatial dimensions d 2 3 and 4 specifically for both aggregation phenomena the authors calculate the fractal dimension dmin nu 1 defined by l approximately rd min where l is the shortest path between two points separated by a pythagorean distance r for cca they find that dmin increases monotonically with d presumably tending toward a limiting value dmin 2 at the upper critical dimensionality dc as found previously for lattice animals and percolation for dla on the other hand they find that dmin 1 within the accuracy of the calculations for d 2 3 and 4 suggesting the absence of an upper critical dimension they also discuss some of the subtle features encountered in calculating dmin for dla

on the geometric structure of non hyperbolic attractors the authors discuss the f alpha spectrum of non hyperbolic attractors of the henon type they elucidate the origin of the phase transition found in a previous paper and give a lower bound to the spectrum in the non hyperbolic phase where kaplan yorke type formulae no longer hold their results disagree with other recent attempts numerical simulations for the henon map agree with analytical estimates

electrical properties of percolation clusters exact results on a deterministic fractal a recursively built deterministic fractal lattice generalising a model proposed by kirkpatrick 1979 is used to examine general electrical properties of percolation clusters in arbitrary dimensions most physical quantities are exactly analytically tractable since the model admits an exact renormalisation group transformation associated with a rational mapping t x of one complex variable the model has one free parameter f the fraction of conducting material which is put equal to the self dual point f 2 3 in two dimensions and chosen to reproduce the numerical values of the exponent ratio t nu in higher dimensions results concern in particular the frequency dependence of the impedance and the loss angle where the authors prove the existence of scaling laws at low and high frequency they also determine exactly the transient response to an arbitrary input signal and relate the distribution of relaxation times of the infinite lattice to well known mathematical objects associated to the rational transform t namely its julia set and its invariant measure the critical amplification of flicker or 1 f resistor noise is also considered it is shown to obey scaling laws with its own critical exponents in agreement with other recent works the relationships to other theoretical models and to experiments on metal insulator mixtures are discussed

fractal properties of the percolating backbone in three dimensions a recursive algorithm to determine the backbone of the two dimensional percolating cluster is adjusted to measure the fractal properties of the backbone of the three dimensional percolating cluster the specific properties measured are the fractal dimensionality of the backbone dbbf 1 75 or 0 04 the chemical dimensionality dt 1 26 or 0 03 and the minimum path dimensionality dmin 1 39 or 0 03

spreading and backbone dimensions of 2d percolation the author presents results of high statistics simulations of the spreading of 2d percolation and of backbones of 2d percolation clusters while the algorithm employed for the spreading is more or less standard for identifying backbones the author uses a new and very efficient recursive algorithm the author uses new critical exponents to test previous conjectures

minireview new results for old percolation abstract percolation theory deals with the formation of clusters in disordered media at the percolation threshold for the first time an infinite cluster appears however research of the last years showed that at this phase transition some old ideas were wrong there can also be two or three clusters spanning from top to bottom even in large two dimensional lattices and the probability of spanning is not given by simple real space renormalization ideas

a real space renormalisation group approach to electrical and noise properties of percolation clusters the migdal kadanoff renormalisation scheme which becomes exact on hierarchical lattices is used to investigate electrical properties of 2d and 3d percolation clusters the author studies in detail the frequency dependence of the conductivity and the loss angle and the amplification of resistance flicker noise this type of noise exhibits critical amplification with its own exponents x and y which are related to the exponent b recently defined by rammal et al 1985

compression unimpaired batch image encryption combining vector quantization and index compression as the network bandwidth has grown rapidly it has become common to share a large number of still images via the internet by means of batch transmission unfortunately most existing methods encrypt only a single image so there is room for improvement in our ability to send batches of images at one time a complete reconstruction of the methods is sometimes necessary especially when considering performance criteria this paper presents a novel batch image encryption algorithm that combines vector quantization vq and additional index compression process to benefit from their computational efficiency and low transmission bandwidth without affecting the original compression rate the experimental results show the performance of this new scheme in terms of compression rate and computational cost

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

renormalisation group study of a disordered model we study the potts model on a diamond hierarchical lattice with random interactions using weak disorder expansions we calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent ap of the pure system becomes positive at ap 0 we find how the logarithmic singularity is modified by the disorder lastly we suggest that this model should present griffiths like singularities

convexity and log convexity for the spectral radius abstract the starting point of this paper is a theorem by j f c kingman which asserts that if the entries of a nonnegative matrix are log convex functions of a variable then so is the spectral radius of the matrix a related result of j cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements the first section of this paper gives a new unified proof of these results and also analyzes exactly when one has strict convexity the second section gives some very simple proofs of results of friedland and karlin concerning min max characterizations of the spectral radius of nonnegative matrices these arguments also yield as will be shown in another paper min max characterizations of the principal eigenvalue of second order elliptic boundary value problems on bounded domains the third section considers the cone k of nonnegative vectors in r n and continuous maps f k k which are homogeneous of degree one and preserve the partial order induced by k the cone spectral radius of such maps is defined and a direct generalization of kingman s theorem to a subclass of such nonlinear maps is given the final section of this paper treats a problem that arises in population biology if k 0 denotes the interior of k and f is as above when can one say that f has a unique eigenvector to within normalization in k 0 a subtle point to be noted is that f may have other eigenvectors in the boundary of k if u k 0 is an eigenvector of f u 1 and g x f x f x when can one say that for any x k 0 g p x the p th iterate of g acting on x converges geometrically to u the fourth section provides answers to these questions that are adequate for many of the population biology problems