on developing fourth order optimal families of methods for multiple roots and their dynamics there are few optimal fourth order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance therefore the first focus of this paper is on developing new fourth order optimal families of iterative methods by a simple and elegant way computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots as far as we know there are no deep study of this kind on iterative methods for multiple roots further using mathematica with its high precision compatibility a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development

a revision of the lyapunov exponent in 1d quadratic maps abstract only misiurewicz points strictly have a lyapunov exponent positive measure in one dimensional 1d quadratic maps hence we represent here the lyapunov exponent of all the misiurewicz points which were found and inventoried by us in a former work as a result of this representation an infinity of alignments of misiurewicz points are obtained and two types of jumps in the values of are found

electrical circuits on mesoscopic sierpinski gaskets a deterministic network of impedances on the sierpinski gasket fractal is considered with particular regard to low generation or mesoscopic systems we study the fractal set of the resonances of the circuit and present calculations on frequency dependent systems the condition of an intermediate size can lead to an oscillatory scaling of the total impedance that disappears in the asymptotic limit several examples are given

chaotic systems counting the number of periods abstract characterization of chaotic motion may proceed both at an averaged macroscopic level using such notions as lyapunov exponents dimensions and entropies and at a microscopic level in the latter case the number of periodic orbits being a topological invariant plays an important role for various one dimensional mappings the counting problem itself has many interesting facets and may be solved more or less completely in different ways recent progress in this counting problem is summarized with the hope that the explicit results obtained may be useful for classification of higher dimensional dissipative chaotic systems

universal scaling behaviour for iterated maps in the complex plane according to the theory of schroder and siegel certain complex analytic maps possess a family of closed invariant curves in the complex plane we have made a numerical study of these curves by iterating the map and have found that the largest curve is a fractal when the winding number of the map is the golden mean the fractal curve has universal scaling properties and the scaling parameter differs from those found for other types of maps also for this winding number there are universal scaling functions which describe the behaviour asn of theq n th iterates of the map whereq n is thenth fibonacci number

third degree anomalies of traub s method traub s method is a tough competitor of newton s scheme for solving nonlinear equations as well as nonlinear systems due to its third order convergence and its low computational cost it is a good procedure to be applied on complicated multidimensional problems in order to better understand its behavior the stability of the method is analyzed on cubic polynomials showing the existence of very small regions with unstable behavior finally the performance of the method on cubic matrix equations arising in control theory is presented showing a good performance

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

on the calculation of misiurewicz patterns in one dimensional quadratic maps abstract in this work we give for the first time a table with all misiurewicz points m n p for low values of the preperiod and period 2 n 8 1 p 5 in one dimensional quadratic maps in the particular case of m n 1 important misiurewicz points which are all placed in the period 1 chaotic band the preperiod values are 2 n 11 a brute force algorithm to obtain all the symbolic sequences patterns of the m n p and a more efficient algorithm to obtain the patterns of m n 1 are also shown

dynamical analysis on cubic polynomials of damped traub s method for approximating multiple roots abstract in this paper the performance of a parametric family including newton s and traub s schemes on multiple roots is analyzed the local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots the fixed and critical points and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work from the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots and also other ones with very unstable behavior

choosing the most stable members of kou s family of iterative methods abstract in this manuscript we analyze the dynamical anomalies of a parametric family of iterative schemes designed by kou et al it is known that its order of convergence is three for any arbitrary value of the parameter but it has order four and it is optimal in the sense of kung traub s conjecture when a specific value is selected among all the elements of this family one can choose this fourth order element or any of the infinite members of third order of convergence if only the speed of convergence is considered however the stability of the methods plays an important role in their reliability when they are applied on different problems this is the reason why we analyze in this paper the dynamical behavior on quadratic polynomials of the mentioned family the study of fixed points and their stability joint with the critical points and their associated parameter planes show the richness of the class and allow us to find members of it with excellent numerical properties as well as other ones with very unstable behavior some test functions are analyzed for confirming the theoretical results

critical points on the boundaries of siegel disks let be a polynomial map of the riemann sphere of degree at least two we prove that if has a siegel disk g on which the rotation number satisfies a diophantine condition then the boundary of g contains a critical point

attracting cycles for the relaxed newton s method we study the relaxed newton s method applied to polynomials in particular we give a technique such that for any n 2 we may construct a polynomial so that when the method is applied to a polynomial the resulting rational function has an attracting cycle of period n we show that when we use the method to extract radicals the set consisting of the points at which the method fails to converge to the roots of the polynomial p z z m c this set includes the julia set has zero lebesgue measure consequently iterate sequences under the relaxed newton s method converge to the roots of the preceding polynomial with probability one

local derivations of nest subalgebras of von neumann algebras in this paper it is proved that every norm continuous linear local derivation of a nest subalgebra of a factor von neumann algebra is a derivation and that every linear 2 local derivation of a nest subalgebra of a factor von neumann algebra is a derivation

characterizing homomorphisms derivations and multipliers in rings with idempotents in certain rings containing non central idempotents we characterize homomorphisms derivations and multipliers by their actions on elements satisfying some special conditions for example we consider the condition that an additive map h between rings mathcal a and mathcal b satisfies h x h y h z 0 whenever x y z in mathcal a are such that xy yz 0 as an application we obtain some new results on local derivations and local multipliers in particular we prove that if mathcal a is a prime ring containing a non trivial idempotent then every local derivation from mathcal a into itself is a derivation

local derivations on certain csl algebras in this paper it is shown that every norm continuous linear local derivation from an arbitrary csl algebra whose lattice is generated by finitely many independent nests into any ultraweakly closed subalgebra which contains the algebra is an inner derivation and that every norm continuous linear local derivation from an arbitrary csl algebra whose lattice is completely distributive into any ultraweakly closed subalgebra which contains the algebra is a derivation

julia sets and bifurcation diagrams for exponential maps on decrit certaines des bifurcations qui apparaissent dans la famille des applications entieres e z exp z pour 1 on sait que j e c on montre qu il y a beaucoup d autres valeurs pour lesquelles ceci arrive

counting the number of periods in one dimensional maps with multiple critical points abstract the problem of counting the number of different periodic orbits in continuous maps of an interval is solved a map with m monotone pieces laps and m 1 critical points may have at most m 1 independent kneading sequences which provide the most convenient parameters for the map when one or more kneading sequences are kept constant or bound to vary simultaneously various degenerated cases of the map arise the number of period n orbits of the general m lap map as various degenerated cases is given by combinations of nink n with k m where nm n is the number of period n orbits of a particular kind of degenerated m lap map with only one kneading sequence the quantity nm n may be calculated or enumerated by many different methods which are all discussed in this paper we also give tabulated values for nm n for m 2 to 7

ac properties of 3d sierpinski gaskets rigorous results the problem of the decimation of a network of impedances on the three dimensional sierpinski gasket is solved the exact map is given and its asymptotic behaviours are studied the most significant invariant subspaces of and the associated submaps are considered this also allows us to address the problem of small size phenomena such as oscillating asymptotic behaviour on this kind of fractal the set of the resonances of the system and the frequency dependence of the total impedance are studied both in the thermodynamic limit and in mesoscopic systems

some properties of mixing repellers applying the thermodynamic formalism to mixing repellers for regular maps the author obtains some rigorous relations between the dimensions of the repellers and the dynamic properties of the transformation on them for a class of one dimensional expanding maps these quantities can be approximated to any desired accuracy by means of the corresponding variables for linear expanding maps which can be computed exactly finally a mathematical foundation and some properties of the generalised dimensions are given

families of rational maps and iterative root finding algorithms in this paper we develop a rigidity theorem for algebraic families of rational maps and apply it to the study of iterative root finding algorithms we answer a question of smale s by showing there is no generally convergent algorithm for finding the roots of a polynomial of degree 4 or more we settle the case of degree 3 by exhibiting a generally convergent algorithm for cubics and we give a classification of all such algorithms in the context of conformal dynamics our main result is the following a stable algebraic family of rational maps is either trivial all its members are conjugate by mobius transformations or affine its members are obtained as quotients of iterated addition on a family of complex tori our classification of generally convergent algorithms follows easily from this result as another consequence of rigidity we observe that the eigenvalues of a nonaffine rational map at its periodic points determine the map up to finitely many choices this implies that bounded analytic functions nearly separate points on the moduli space of a rational map

a general view of pseudoharmonics and pseudoantiharmonics to calculate external arguments of douady and hubbard harmonics give us a compact formula and a powerful tool in order to calculate the external arguments of the last appearance hyperbolic components and misiurewicz points of the mandelbrot set in some particular cases antiharmonics seem however to have no application in this paper we give a general view of pseudoharmonics and pseudoantiharmonics as a generalization of harmonics and antiharmonics pseudoharmonics turn out to be a more powerful tool than harmonics since they allow the calculation of external arguments of the mandelbrot set in many more cases likewise unlike antiharmonics pseudoantiharmonics turn out to be a powerful tool to calculate external arguments of the mandelbrot set in some cases

local derivations on operator algebras abstract when attempting to find sufficient conditions for a linear mapping to be a derivation an obvious candidate is the concept of a local derivation local derivations on operator algebras have been investigated in recent papers of kadison j algebra130 1990 494 509 and larson and sourour proc symp pure math 51 1990 187 194 a local derivation is a norm continuous linear map from an operator algebra a into an a bimodule m which agrees with some derivation at each point in the algebra we show that if a is the direct limit of finite dimensional csl algebras via extendable embeddings e g a triangular af algebra then a local derivation on a must be a derivation further we show that for many finite dimensional operator algebras any inner local derivation must be an inner derivation

on the multiplier of a repelling fixed point we estimate the multiplier of a repelling fixed point with rational rotation number for a polynomial in one complex variable we show that a canonical branch of the logarithm of lies in a small disk tangent to the imaginary axis the radius of the disk is determined by the degree of the polynomial the rotation number of the fixed point and the escape rates and external arguments of the critical values

dynamics of a family of third order iterative methods that do not require using second derivatives the purpose of this article is to present results that amount to a description of the conjugacy classes of three third order root finding iterative methods that do not require the use of second derivatives for their formulation for complex polynomials of degrees two three and four for degrees two and three a full description of the conjugacy classes is accomplished in each case by a one parameter family of polynomials this is done in such a way that when one applies one of these three root finding iterative methods to the elements of these parametrized families a family of iterative methods is obtained in such a way that its dynamics represents up to conjugacy the dynamics of the corresponding iterative root finding method applied to any complex polynomial having the same degree for degree four analogous partial results are obtained

on the dynamics of laguerre s iteration z n 1 abstract the laguerre algorithm for computing the zeros of polynomial equations is well known many proofs of the global convergence of this method for the class of real polynomials with all real roots and starting from real initial conditions exist in this article the global behavior of the laguerre iteration is studied when applied to zn 1 for this class of polynomials an almost complete description of the dynamics of laguerre is rendered

the generalized mandelbort julia sets from a class of complex exponential map we have generalized the baker devaney and romera s work and constructed a series of generalized mandelbort julia sets in abbreviated form generalized m j sets from the complex exponential map using the experimental mathematics method we have innovated as follows present the theoretic proof about the explosion of the generalized j sets for complex index number theoretically analyze the symmetry and periodicity of the generalized m j sets present a new attaching rule described the distributing of periodicity petal of generalized m sets for complex index number find abundant structure information of the generalized j sets contained in the generalized m sets for complex index number find that the speed of fractal growth in generalized m j sets for complex index number is faster than that of generalized m j sets for real index number the parameter value l 0 decides the speed of the fractal growth and the fractal growth in generalized m sets for complex index number points tends to the multifurcation and misiurewicz point

julia sets of the schroder iteration functions of a class of one parameter polynomials with high degree in this paper the theory of julia sets of schroder iteration functions is introduced the julia sets of the schroder functions of a one parameter family polynomials with high degree are constructed through iteration method and their structures are analyzed consequently the following results are found in the study 1 the julia sets of the schroder iteration functions of a one parameter family polynomials with high degree contain the structure of classical mandelbrot like set 2 the orbits of the critical points may escape from the zero points of the corresponding polynomial to converge to the k cycle attractive basin or the extra fixed points 3 if critical points on parameter plane are selected to construct julia sets on dynamics plane then attractive k cycle basin will emerge while it will not emerge if no critical points are selected 4 the extra fixed points may be repulsive litmusless or attractive but the former takes the major role and 5 the julia sets of the schroder iteration functions have symmetry

the complex dynamics of newton s method for a double root we show that the relaxed newton s method for finding the roots of a cubic with one double root is conjugate by a linear fractional transformation on the p iemmm sphere to the iterations of the quadratic p z z 2 0 75

fuzzy model based clustering and its application in image segmentation a fuzzy generalized gaussian density ggd segmentation model is proposed a ggd based agglomerative fuzzy algorithm is developed a two stage fuzzy ggd segmentation algorithm is proposed this paper proposes a novel fuzzy model based unsupervised learning algorithm with boundary correction for image segmentation we propose a fuzzy generalized gaussian density ggd segmentation model and the ggd based agglomerative fuzzy algorithm for grouping image pixels the merits of algorithm are that it is not sensitive to initial parameters and that the number of groups can be estimated via the validation technique to minimize the objective function of the model we define a dissimilarity measure based on the kullbackleibler divergence of the ggds that computes the discrepancy between ggds in the space of generalized probability distributions to effectively segment images with various textures we propose a two stage fuzzy ggd segmentation algorithm the first stage adopts the proposed fuzzy algorithm to obtain initial segmentation and the second stage improves initial segmentation by image boundary correction experimental results show that our proposed method has a promising performance compared with existing approaches

an iterated implicit complex map abstract iterated complex maps defined by a root of a biquadratic equation g z z 0 are studied numerical studies suggest conjugacy functions with differentiable natural boundaries and maps having island chains occupying much of the riemann sphere an analogy with hamiltonian systems is discussed

parametric generalized gaussian density estimation the primary objective of this paper is to compare the large sample as well as the small sample properties of different methods for estimating the parameters of a three parameter generalized gaussian distribution three estimators namely the moment method mm the maximum likelihood ml and the moment newton step mns estimators are considered the applicability of general asymptotic optimality results of the efficient ml and mns estimation techniques is studied in the generalized gaussian context the asymptotic normal distributions of the estimators are obtained the asymptotic relative superiority of the ml estimator or its variant the mns estimator over the moment method is studied in terms of asymptotic relative efficiency based on this study it is concluded that deviations from normality in the underlying distribution of the data necessitate the use of the efficient ml or mns methods in the small sample case a detailed comparative study of the estimators is made possible by extensive monte carlo simulations from this study it is concluded that the maximum likelihood method is found to be significantly superior for heavy tailed distributions in a region of the parameter space corresponding to the vicinity of the gaussian distribution the moment method compares well with the other methods further the mns estimator is shown to perform best for light tailed distributions the simulation results are shown to lend support to analytically derived asymptotic results for each of the methods

renormalization group analysis of quasi periodicity in analytic maps analytic maps of the form f z e 2 pi i omega z mathcal o z 2 display quasiperiodicity when satisfies a diophantine condition quasiperiodic motion is confined to a neighborhood of the origin known as a siegel domain the boundary of this domain obeys universal scaling relations in this paper we investigate these scaling relations through a renormalization group analysis and we discuss singularities and asymptotic form of the scaling function

diophantine conditions imply critical points on the boundaries of siegel disks of polynomials let f be a polynomial map of the riemann sphere of degree at least two we prove that if f has a siegel disk g on which the rotation number satisfies a diophantine condition then either the boundary b of g contains a critical point or b is a lakes of wada indecomposable continuum with one of the lakes containing a critical point consequently if the boundary b of g has only 2 complementary domains then b contains a critical point we also show without any assumption on the rotation number that each proper nondegenerate subcontinuum of the boundary b of g is tree like and any other bounded complementary domain of b is a preperiodic component of the grand orbit of g finally we establish some conditions under which b contains no periodic point

prevalence a translation invariant almost every on infinite dimensional spaces we present a measure theoretic condition for a property to hold almost everywhere on an infinite dimensional vector space with particularemphasis on function spaces such as c k and l p like the concept of lebesgue almost every on an infinite dimensional spaces our notion of prevalence is translation invariant instead of using a specific measure on the entire space we define prevalence in terms of the class of all probability measures with compact support prevalence is a more appropriate condition than the topological concepts of open and dense or generic when one desires a probabilistic result on the likelihood of a given property on a function space

complex dynamics of derivative free methods for nonlinear equations the dynamical behavior of two iterative derivative free schemes steffensen and m4 methods is studied in case of quadratic and cubic polynomials the parameter plane is analyzed for both procedures on quadratic polynomials different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients the property of immersion of the basins of attraction in all cases is analyzed

wavelet based texture retrieval using generalized gaussian density and kullback leibler distance we present a statistical view of the texture retrieval problem by combining the two related tasks namely feature extraction fe and similarity measurement sm into a joint modeling and classification scheme we show that using a consistent estimator of texture model parameters for the fe step followed by computing the kullback leibler distance kld between estimated models for the sm step is asymptotically optimal in term of retrieval error probability the statistical scheme leads to a new wavelet based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized gaussian density ggd and on the existence a closed form for the kld between ggds the proposed method provides greater accuracy and flexibility in capturing texture information while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates e g from 65 to 77 compared with traditional approaches while it retains comparable levels of computational complexity

research on fractal structure of generalized m j sets utilized lyapunov exponents and periodic scanning techniques abstract in order to show details of fractal structure of mandelbrot set precisely lyapunov exponents and periodic scanning techniques have been brought forward by shirriff and welstead this paper generalizes these two techniques and puts forward periodicity orbit search and comparison technique which can be used to discuss the relationship of the generalized mandelbrot julia sets the generalized m j sets adopting the techniques mentioned above and the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized m j sets generated from the complex mapping z z c r and explores structure and distributing of periodicity petal and topological law of periodicity orbits of the generalized m sets and finds that the generalized m set contains abundant information of structure of the generalized j sets by founding the whole portray of the generalized j sets based on the generalized m set qualitatively furthermore the physical meaning of the generalized m j sets have been expounded

operating with external arguments in the mandelbrot set antenna the external argument theory of douady and hubbard allows us to know both the potential and the field lines in the exterior of the mandelbrot set nonetheless there are no explicit formulae to operate with external arguments and the external argument theory is difficult to apply in this paper we introduce some tools in order to obtain formulae to operate with external arguments in the mandelbrot set antenna thus we introduce the harmonic tool to calculate both the external arguments of the period doubling cascade hyperbolic components and the external arguments of the last appearance hyperbolic components likewise we introduce composition rules applied to external arguments that with the aid of the concept of heredity allows the calculation of all the external arguments that constitutes the family tree of a given external argument

construction of fourth order optimal families of iterative methods and their dynamics in this paper we propose a general class of fourth order optimal multi point methods without memory for obtaining simple roots this class requires only three functional evaluations viz two evaluations of function f xn f yn and one of its first order derivative f xn per iteration further we show that the well known ostrowski s method and king s family of fourth order procedures are special cases of our proposed schemes one of the new particular subclasses is a biparametric family of iterative methods by using complex dynamics tools its stability is analyzed showing stable members of the family further on one of the parameters is fixed and the stability of the resulting class is studied on the other hand the accuracy and validity of new schemes is tested by a number of numerical examples by comparing them with recent and classical optimal fourth order methods available in the literature it is found that they are very useful in high precision computations

a dynamical meaning of fractal dimension when two atlractors of a dynamical system have a common basin boundary b small changes in initial conditions which lie near b can result in radically different long term behavior of the trajectory a quantitative description of this phenomenon is obtained in terms of the fractal dimension of the basin boundary b

julia sets and complex singularities in hierarchical ising models we study the analytical continuation in the complex plane of free energy of the ising model on diamond like hierarchical lattices it is known 12 13 that the singularities of free energy of this model lie on the julia set of some rational endomorphismf related to the action of the migdal kadanoff renorm group we study the asymptotics of free energy when temperature goes along hyperbolic geodesics to the boundary of an attractive basin off we prove that for almost all with respect to the harmonic measure geodesics the complex critical exponent is common and compute it

on the modeling of small sample distributions with generalized gaussian density in a maximum likelihood framework the modeling of sample distributions with generalized gaussian density ggd has received a lot of interest most papers justify the existence of ggd parameters through the asymptotic behavior of some mathematical expressions i e the sample is supposed to be large in this paper we show that the computation of ggd parameters on small samples is not the same as on larger ones in a maximum likelihood framework we exhibit a necessary and sufficient condition for the existence of the parameters we derive an algorithm to compute them and then compare it to some existing methods on random images of different sizes

on the dynamics of the euler iterative function abstract the dynamics of euler s third order iterative method which is used to find roots of non linear equations applied to complex polynomials of degrees three and four is studied the conjugacy classes of this method are found explicitly

the hausdorff dimension of the boundary of the mandelbrot set and julia sets it is shown that the boundary of the mandelbrot set m has hausdorff dimension two and that for a generic c e am the julia set of z i z2 c also has hausdorff dimension two the proof is based on the study of the bifurcation of parabolic periodic points

the julia set of newton s method for multiple root abstract in this paper we analyze the julia set of newton method for multiple roots construct the julia sets of standard relaxed and multiple roots through the experimental mathematics method we drew the following conclusion 1 the julia sets of above methods for f z z z 1 has time rotation symmetry and its center is origin 2 the multiple roots domain of attraction of these kinds of julia sets are sensitive to 3 there is not simple root domain of attraction in relax method because z the root of f z is neutral or repelling fixed point of f z 4 is not the fixed point of f z so multiple root s julia set consists of a great number of attraction domain of multiple and simple roots 5 the experimental errors and truncation of coefficients cause the minimal effect to multiple root the more to relax the maximal to standard newton method

on the iteration of a rational function computer experiments with newton s method using newton s method to look for roots of a polynomial in the complex plane amounts to iterating a certain rational function this article describes the behavior of newton iteration for cubic polynomials after a change of variables these polynomials can be parametrized by a single complex parameter and the newton transformation has a single critical point other than its fixed points at the roots of the polynomial we describe the behavior of the orbit of the free critical point as the parameter is varied the julia set points where newton s method fail to converge is also pictured these sets exhibit an unexpected stability of their gross structure while the changes in small scale structure are intricate and subtle

spirals in the mandelbrot set ii abstract the alpha function is used to quantify the asymptotic structure of the various branches and embedded spirals around the left hand side of the main cardioid in the mandelbrot set

a stable family with high order of convergence for solving nonlinear equations recently li et al 2014 have published a new family of iterative methods without memory with order of convergence five or six which are not optimal in the sense of kung and traub s conjecture therefore we attempt to modify this suggested family in such a way that it becomes optimal to this end we consider the same two first steps of the mentioned family and furthermore we introduce a better approximation for f z in the third step based on interpolation idea as opposed to the taylor s series used in the work of li et al theoretical dynamical and numerical aspects of the new family are described and investigated in details

on local connectivity for the julia set of rational maps newton s famous example we show that newton s cubic methods famous rational maps have a locally connected julia set except in some very specific cases in particular when those maps are infinitely renormalizable their julia set is locally connected and contains small copies of nonlocally connected quadratic julia sets this also holds when newton s method is renormalizable and has cremer points unlike the polynomial case after a dynamical description we show the necessity of the brjuno condition within this family

local derivations and local automorphisms in this paper we show that if l is a completely distributive commutative subspace lattice or a j subspace lattice then the space of all bounded derivations of algl is reflexive we also study when local automorphisms on some algebras are automorphisms

braiding of the attractor and the failure of iterative algorithms le mouvement de l attracteur dans une famille stable d applications rationnelles determine un groupe de tresses sur la sphere de riemann on montre que le groupe correspondant des classes d application est soit reductible soit fini soit fixe l un des attracteurs ceci conduit a un critere topologique d existence des bifurcations dans les algorithmes iteratifs de recherche de racines bases sur des applications rationnels

wavelet based level set evolution for classification of textured images we present a supervised classification model based on a variational approach this model is specifically devoted to textured images we want to get a partition of an image composed of texture regions separated by regular interfaces each kind of texture defines a class we use a wavelet packet transform to analyze the textures characterized by their energy distribution in each sub band in order to have an image segmentation according to the classes we model the regions and their interfaces by level set functions we define a functional on these level sets whose minimizers define the optimal classification according to texture a system of coupled pdes is deduced from the functional by solving this system each region evolves according to its wavelet coefficients and interacts with the neighbor regions in order to obtain a partition with regular contours experiments are shown on synthetic and real images

a computer algorithm for determining the hausdorff dimension of certain fractals a fractal is a set which has nonintegral hausdorff dimension computation of the dimension directly from the definition would be very time consuming on a computer however the dimension can be computed using newton s method if there exists a self expanding map on the set this technique is applied to compute the dimension of the julia set of the quadratic mapping z z2 c for small real values of c 1 fractals and hausdorff dimension b mandelbrot 4 introduced the word fractal as a set for which the hausdorff besicovitch dimension strictly exceeds the topological dimension whereas the topological dimension of any subset of the plane is either one or two the hausdorff dimension may be nonintegral physicists 7 use the word strange in this context informally the hausdorff dimension of a subset x of a metric space can be pictured by overlaying an n by n gridwork of boxes on x for arbitrarily large values of n in this manner x is covered by n2 boxes if x is linear then only n of the boxes intersect x and x has hausdorff dimension one if x covers most of the plane then approximately n2 of the boxes intersect x and x has hausdorff dimension two if x falls between the first and second case then x intersects nd boxes for some value of d between one and two and x is a fractal with hausdorff dimension d in other words if x has dimension d then approximately nd boxes of size 1 n are needed to cover x this might be of interest when drawing x on some coarse device such as a graphics terminal where a point on the device is in reality a ball of size 1 n strictly speaking the gridwork picture describes the minkowski dimension it is equal to the hausdorff dimension in all nice cases which includes all the sets discussed in this paper more formally definition let c e be a covering on x by countably many balls bj ri iei of radius ri 0 form the sum ii ri take the infimum of the sum over all coverings c e define a function ha by taking the limit of the infimums as e approaches zero notationally this says h x lim inf erg e o kzei this is a way of measuring the area needed to cover x by small balls with the convention that a ball of radius r has area ra if af is too small then h x is infinite if af is too large then h x is zero there is a unique value where 1988 american mathematical society 0025 5718 88 1 00 25 per page 291 received september 17 1985 revised july 31 1987 1980 mathematics subject classification 1985 revision primary 58f21 30d05 this content downloaded from 207 46 13 128 on wed 07 sep 2016 05 52 01 utc all use subject to http about jstor org terms

on the modeling of dct and subband image data for compression image subband and discrete cosine transform coefficients are modeled for efficient quantization and noiseless coding quantizers and codes are selected based on laplacian fixed generalized gaussian and adaptive generalized gaussian models the quantizers and codes based on the adaptive generalized gaussian models are always superior in mean squared error distortion performance but generally by no more than 0 08 bit pixel compared with the much simpler laplacian model based quantizers and noiseless codes this provides strong motivation for the selection of pyramid codes for transform and subband image coding

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

statistical properties of bit plane probability model and its application in supervised texture classification the modeling of wavelet subband histograms via the product bernoulli distributions pbd has received a lot of interest and the pbd model has been applied successfully in texture image retrieval in order to fully understand the usefulness and effectiveness of the pbd model and its associated signature namely the bit plane probability bp signature on image processing applications we discuss and investigate some of their statistical properties these properties would help to clarify the sufficiency of the bp signature to characterize wavelet subbands which in turn justifies its use in real time applications we apply the bp signature on supervised texture classification problem and experimental results suggest that the weighted l1 norm rather than the standard l1 norm should be used for the bp signature comparative classification experiments show that our method outperforms the current state of the art generalized gaussian density approaches

texture classification using refined histogram in this correspondence we propose a novel efficient and effective refined histogram rh for modeling the wavelet subband detail coefficients and present a new image signature based on the rh model for supervised texture classification our rh makes use of a step function with exponentially increasing intervals to model the histogram of detail coefficients and the concatenation of the rh model parameters for all wavelet subbands forms the so called rh signature to justify the usefulness of the rh signature we discuss and investigate some of its statistical properties these properties would clarify the sufficiency of the signature to characterize the wavelet subband information in addition we shall also present an efficient rh signature extraction algorithm based on the coefficient counting technique which helps to speed up the overall classification system performance we apply the rh signature to texture classification using the well known databases experimental results show that our proposed rh signature in conjunction with the use of symmetrized kullback leibler divergence gives a satisfactory classification performance compared with the current state of the art methods

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

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

frontiers in complex dynamics rational maps on the riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems first rational maps are complexanalytic so a broad spectrum of techniques can contribute to their study quasiconformal mappings potential theory algebraic geometry etc the rational maps of a given degree form a finite dimensional manifold so exploration of this parameter space is especially tractable finally some of the conjectures once proposed for smooth dynamical systems and now known to be false seem to have a definite chance of holding in the arena of rational maps in this article we survey a small constellation of such conjectures centering around the density of hyperbolic rational maps those which are dynamically the best behaved we discuss some of the evidence and logic underlying these conjectures and sketch recent progress towards their resolution

external arguments for the chaotic bands calculation in the mandelbrot set abstract in this paper we study the chaotic bands of any mandelbrot set hyperbolic component we use external arguments in order to identify the hyperbolic components if we use harmonics as a tool we can directly calculate the chaotic bands indeed as we clearly show here the harmonics of the external arguments of a given hyperbolic component gene are the external arguments of the last appearance hyperbolic components of the chaotic bands corresponding to the gene likewise we explain some differences in the chaotic region of cardioids and discs

symbolic sequences of one dimensional quadratic maps points abstract in previous works we introduced the symbolic sequence of the orbit of a misiurewicz point of a one dimensional quadratic map and formulae to calculate the symbolic sequences of the orbits of the tip and the cusp points in the mandelbrot set antenna an l map in this work we generalize these expressions to any map type and we present simple formulae to directly calculate the symbolic sequences of chaotic bands merging points pitchfork bifurcation points and stable periodic points in one dimensional quadratic maps to conclude some considerations about the notation of the accumulation points are accomplished

the iteration of cubic polynomials part i the global topology of parameter space fonctions univalentes en dynamique analytique complexe torsion de la structure complexe topologie globale de l espace parametre

a mandelbrot set for pairs of linear maps the set of points a s 1 s s 2 s 3 for all sequences of and generically a fractal for example a 1 3 is the classical cantor set and a 1 2 i 2 is a dragon curve this set of fractals can be classified in terms of an associated mandelbrot set d s s a s is disconnected the structure of d and its boundary are investigated

generalized julia sets from a non analytic complex mapping abstract the method constructing the julia sets from a simple non analytic complex mapping developed by michelitsch and rossler was expanded according to the complex mapping expanded by the author a series of the generalized julia sets for real index number were constructed using the experimental mathematics method combining the theory of analytic function of one complex variable with computer aided drawing the fractal features and evolutions of the generalized julia sets are studied the results show 1 the geometry structure of the generalized julia sets depends on the parameters r and c 2 the generalized julia sets have symmetry and fractal feature 3 the generalized julia sets for decimal index number have discontinuity and collapse and their evolutions depend on the choice of the principal range of the phase angle

misiurewicz points in one dimensional quadratic maps abstract misiurewicz points are constituted by the set of unstable or repellent points sometimes called the set of exceptional points these points which are preperiodic and eventually periodic play an important role in the ordering of hyperbolic components of one dimensional quadratic maps in this work we use graphic tools to analyse these points by measuring their preperiods and periods and by ordering and classifying them

local lie derivations of factor von neumann algebras abstract let a be a factor von neumann algebra acting on a complex hilbert space h with dim a 2 we show that each local lie derivation from a into itself is a lie derivation

selective solutions to transcendental equations abstract this paper presents a combination of global iterative methods based on the fatou julia theory and local methods to find selected roots of elementary transcendental equations z f z c z and c complex that occur in complex sturm liouville eigenvalue problems in dielectric spectroscopy and in orbit determination suitable starting values for the iteration function z n 1 f z n c and appropriate regions for each determination of the inverse iteration function z n f 1 z n c are presented convergence criteria are derived from the facts that f has very few attractive fixed points and that the attractive fixed points of f 1 have relatively large basins of attraction in the above mentioned regions certain fixed points of f can be reached quickly by means of a local method like newton s method it is shown by means of digital figures that in general newton s method may lead to attractive cycles or to unpredictable roots when the starting values are near the fatou julia set convergence to parasitic roots or even to strange attractors may occur with iterative methods of higher order

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

low complexity root finding iteration functions with no derivatives of any order of convergence in this paper a procedure to design steffensen type methods of different orders for solving nonlinear equations is suggested by using a particular divided difference of first order we can transform many iterative methods into derivative free iterative schemes holding the order of convergence of the departure original method numerical examples and the study of the dynamics are made to show the performance of the presented schemes and to compare them with another ones

misiurewicz point patterns generation in one dimensional quadratic maps abstract in a family of one dimensional quadratic maps misiurewicz points are unstable and the orbits of such a points are repulsive on the contrary the orbits of superstable periodic points are attractive here we study the patterns of the symbolic sequences of both misiurewicz and superstable periodic points and show that a misiurewicz point pattern can be obtained as the limit of the sum of a superstable periodic orbit pattern plus itself or some of its heredity transmitters repeated an infinite number of times inversely when a misiurewicz point pattern is given we also show that it is possible to find both the superstable periodic orbit pattern and the heredity transmitters that generate such a pattern

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed