a highly efficient algorithm for the generation of random fractal aggregates abstract a technique to generate random fractal aggregates where the fractal dimension is fixed a priori is presented the algorithm utilizes the box counting measure of the fractal dimension to determine the number of hypercubes required to encompass the aggregate on a set of length scales over which the structure can be defined as fractal at each length scale the hypercubes required to generate the structure are chosen using a simple random walk which ensures connectivity of the aggregate the algorithm is highly efficient and overcomes the limitations on the magnitude of the fractal dimension encountered by previous techniques

control of wave processes with distributed controls supported on a subregion it is proved that solutions of one dimensional wave equations satisfying general boundary conditions at the ends of a bounded interval i can be exactly controlled to any finite energy state by means of distributed controls which vanish outside of any fixed nonempty subinterval of i an example is given which shows that no such general analogous result can hold in higher dimensions in this case for a spherical region those states are characterized which can be exactly controlled to zero by means of controls supported in an annulus within the region it is found that very strong controllability obtains when the controls are distributed near the boundary but that only rather weak controllability is possible with controls supported in an interior annulus applications of these results to boundary control problems in annular regions are also discussed

adaptive sliding mode control in discrete time systems abstract discrete time sliding mode control is considered the case of known parameters is first analyzed leading to a new definition of the so called equivalent control as the piecewise constant control that reduces to zero in finite time the distance of the system state from the sliding manifold in the presence of bounded parametric uncertainties an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented the main feature of this approach is the reduction of the order of the relevant error equation and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process

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

self dual fractal models for the low field hall effect near percolation threshold fractal lattices with the self duality property are proposed to imitate the geometric texture of two dimensional percolating networks at percolation threshold the exponents describing the power law dependence on the scale length of the hall and ohmic conductivities are found the exponent for the hall conductivity agrees with twice that for the ohmic conductivity the model is extended to describe the approach towards the threshold it is found that the model shows the typical percolation behaviour as a function of a parameter p the bond concentration

hierarchical ensembles random fractals flow fractals and the renormalisation group hierarchical ensembles possess exactly renormalisable partition functions examples studied in this work are iterative geometric constructions which at criticality give random self similar fractals the ensembles include novel non self similar constructions termed flow fractals here the simple criticality of these ensembles is analysed and the self similar fractals are found to be homogeneous a multiple weight ensemble the ising snowflake is introduced the transfer matrix of fractals is defined via the renormalisation group a discussion and interpretation is given of the eigenvalues of the transfer matrix fractals for the ising snowflake

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

geometrical properties of aggregates with tunable fractal dimension we have computed geometrical characteristics of large clusters up to 32 768 particles obtained by a hierarchical cluster cluster aggregation computer model in three dimensions the off lattice variable d model using a box counting method we have calculated the fractal dimensions of the surface and the perimeter of their two dimensional projections as a function of their fractal dimension d by diagonalizing the radius of gyration tensor we have obtained numerical estimates for the intrinsic anisotropy coefficients ratios of the eigenvalues and we have proposed analytical expressions to describe their behaviour as a function of the fractal dimension

a variational approach to constrained controllability for distributed systems abstract we consider linear distributed control systems of the form y t a y t b u t where a generates a strongly continuous semigroup e t a t 0 on an infinite dimensional hilbert space y we suppose that the control operator b is bounded from the hilbert control space u to y taking into account eventual control constraint such as saturation we study the problem of exact controllability by using a variational approach applications to hyperbolic like systems of the form z t a z t b u t are treated

topological and geometrical properties of dla clusters three new exponents are calculated for diffusion limited aggregates in two dimensions via computer simulation the 1 n 0 limit gives zeta 1 52 nu 0 91 and dw 2 56 these results confirm martin s conjecture d zeta nu and are consistent with previous work indicating that topological rather than geometrical properties of random fractals are responsible for variations in fractal dimension diffusion on dla clusters is anomalous with an exponent that is consistent with the alexander orbach conjecture and satisfies the einstein relation

non linear discrete variable structure systems in quasi sliding mode abstract the problem of inducing convergent quasi sliding regimes on smooth state space surfaces of non linear single input single output discrete time controlled systems is addressed in full generality a suitable extension of the notion of relative degree is used in establishing the most salient features of quasi sliding motions in non linearly controlled systems several examples are given

the structure of two dimensional witten sander aggregates a relatively large number 102 103 of reasonably large about 105 particles or sites two dimensional witten sander aggregates are simulated using new algorithms this enables the reduction of statistical errors by an order of magnitude and provides an opportunity to determine some new quantities describing in more detail the structure of witten sander clusters a quantitate description of the distortion of large lattice based witten sander clusters into a diamond like shape is provided the orientational correlation in the bond directions for off lattice witten sander clusters is also measured this quantity has a power law dependence on distance with an exponent of about 0 37

backbone and elastic backbone of percolation clusters obtained by the new method of burning we introduce a method of obtaining information about percolation clusters in which the clusters are burned in different ways this method yields the backbone and the elastic backbone their number of loops shortest path and other quantities it works in any dimension and can be applied also to other clusters we obtain accurate estimates for the backbone exponents in two and three dimensions

variable structure control design for uncertain discrete time systems the main differences between the designs of discrete time variable structure systems vss and continuous time vss are the determination of the switching hyperplane and the satisfaction of the hitting sliding condition these differences yield many difficulties in the design of sliding mode control for the discrete time vss this note tries to overcome these difficulties and design a simple sliding mode control for a single input discrete time vss such that not only the discrete time uncertain system is stabilized robustly but also the chattering along the sliding mode is reduced explicitly instead of the conventional switching hyperplane in the discrete time case a switching region which includes the hyperplane s sub 0 and its neighborhood is determined and used the determination of the switching region is to locate the equilibrium point of the nominal subsystem on each hyperplane s sub p outside the switching region such that the state motions inside and outside the switching region will occur alternately until the state of the closed loop system reaches the origin moreover we prove that the robustness property is retained whenever the uncertainty satisfies a standard matching condition

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

bayes smoothing algorithms for segmentation of binary images modeled by markov random fields a new image segmentation algorithm is presented based on recursive bayes smoothing of images modeled by markov random fields and corrupted by independent additive noise the bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel given the total noisy image in a recursive way the a posteriori distribution together with a criterion of optimality then determine a bayes estimate of the scene the algorithm presented is an extension of a 1 d bayes smoothing algorithm to 2 d and it gives the optimum bayes estimate for the scene value at each pixel computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm in particular the scene noiseless image is modeled as a markov mesh random field a special class of markov random fields and the bayes smoothing algorithm is applied on overlapping strips horizontal vertical of the image consisting of several rows columns it is assumed that the signal scene values vector sequence along the strip is a vector markov chain since signal correlation in one of the dimensions is not fully used along the edges of the strip estimates are generated only along the middle sections of the strips the overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image the bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel discrete or continuous random variables

exact controllability of the one dimensional wave equation with locally distributed control the one dimensional wave equation with variable wave speed and locally distributed control is considered it is shown that the adjoint system is observable using a multiplier method with a multiplier being the solution of an ordinary differential equation it is also shown that a sufficient condition for exact controllability is that a related minimization problem always has an optimal solution since the objective function for this minimization problem would be coercive if the adjoint system is observable this establishes the exact controllability of the original system

lessons from an example in on the stability of discrete time sliding mode control systems initial conditions are presented for which the indicated example in the above paper by sarpturk et al ibid vol ac 32 1987 is shown to fail to meet the paper s theoretical requirements the importance of this error is that the example now represents a counterexample to the suggested form of the sliding mode control demonstrates a necessary restriction on any such quasi sliding mode control and illustrates that restrictions presented in another paper are not global

a fast and accurate implementation of tunable algorithms used for generation of fractal like aggregate models abstract in many branches of science experiments are expensive require specialist equipment or are very time consuming studying the light scattering phenomenon by fractal aggregates can serve as an example light scattering simulations can overcome these problems and provide us with theoretical additional data which complete our study for this reason a fractal like aggregate model as well as fast aggregation codes are needed until now various computer models that try to mimic the physics behind this phenomenon have been developed however their implementations are mostly based on a trial and error procedure such approach is very time consuming and the morphological parameters of resulting aggregates are not exact because the postconditions e g the position error cannot be very strict in this paper we present a very fast and accurate implementation of a tunable aggregation algorithm based on the work of filippov et al 2000 randomization is reduced to its necessary minimum our technique can be more than 1000 times faster than standard algorithms and the position of a new particle or a cluster is calculated with algebraic methods therefore the postconditions can be extremely strict and the resulting errors negligible e g the position error can be recognized as non existent in our paper two different methods which are based on the particle cluster pc and the cluster cluster cc aggregation processes are presented

comments on the control of robot manipulators with bounded input with reply the present author demonstrates 1 that the optimal decision strategy ods proposed in the paper by m w spong and j s thorp ieee trans automat contr vol ac 31 p 483 90 1986 is in fact a specific case of an optimal aim strategy oas with special aim state and system state assignments and 2 that the primal dual method employed in the same paper can be replaced by a more direct more efficient discrete time control algorithm based on fixed point iteration or by a more complete more exact continuous time control law based on fixed point feedback for the class of problems under discussion however the authors special assignments represent a significant application of optimal aim notions spong and thorp point out that although the optimal decision strategy ods that they use in their paper does not appear to be a special case of oas as originally defined it can be included within the framework of more recent formulations of oas in fact it appears that the two methods as currently defined are essentially equivalent

a regular random fractal model for cluster numbers and structure in percolation a regular random fractal intermediate between statistical fractals and deterministic fractals is presented to imitate the geometric texture at and near percolation threshold the model is constructed on the square lattice via a rule of bond occupation with use of position space renormalisation group it shows the typical percolation behaviour as a function of a parameter p the bond concentration the critical bond concentration correlation length exponent and scaling property of the cluster size distribution are found the scaling relations between critical exponents for cluster numbers and structure are shown to be exactly satisfied the fractal dimension of its cutting bonds agrees with the inverse of the connectedness length exponent at criticality

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

family of growth fractals with continuously tunable chemical dimension we introduce a new class of statistical growth fractals which is of interest because the chemical dimension d is continuously tunable we also study other exponents charac terising these fractals there has been considerable recent interest in uncovering the fashion in which the familiar laws of physics are modified for fractal objects in part because of the large number of important realisations of fractals in nature l 81 it has only recently become appreciated that the physics of fractals is determined by more than just the fractal dimension df which describes how the cluster mass n scales with the cluster radius r

diffusion on regular random fractals we study random walks on structures intermediate to statistical and deterministic fractals called regular random fractals constructed introducing randomness in the distribution of lacunas of sierpinski carpets random walks are simulated on finite stages of these fractals and the scaling properties of the mean square displacement of n step walks are analysed the anomalous diffusion exponents obtained are very near the estimates for the carpets with the same dimension this result motivates a discussion on the influence of some types of lattice irregularity random structure dead ends lacunas on based on results on several fractals we also propose to use these and other regular random fractals as models for real self similar structures and to generalize results for statistical systems on fractals

robust control of discretized continuous systems using the theory of sliding modes the idea of sliding mode control smc as a robust control technique is utilized to control systems where the dynamics can be described by xdot t a a x t b b u t d t where a b and d t characterize unknown plant parameters and unexpected disturbances respectively the analysis is described in the discrete form using the euler operator the proposed controller regards the influence of unknown disturbances and parameter uncertainties as an equivalent disturbance and generates a control function estimate to cancel their influence by the mechanism of time delay the states of the uncertain plant are steered from an arbitrary initial state to a stable surface s 0 and the plant output is subsequently regulated one feature of the control is that the sliding conditions are satisfied without the discontinuous control action used in classical smc it therefore retains the positive features of smc without the disadvantage of control chattering the controller has been studied through s

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

a cluster cluster aggregation model with tunable fractal dimension a hierarchical cluster cluster aggregation computer model is introduced which allows one to build random fractal aggregates on a d dimensional lattice with a fractal dimension fixed a priori the algorithm works iteratively by sticking aggregates of the same number of particles at the correct centre to centre distance in order to recover the desired scaling with the more efficient versions of the model any fractal dimension ranging from 1 up to a d dependent upper limit dm d can be obtained one estimates dm 2 approximately 1 80 or 0 03 and dm 3 approximately 2 55 or 0 04 calculations up to d 8 show that the ratio dm d d decreases as d increases

the coastline and lake shores on a fractal island we compute the fractal dimensions of the hulls or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures our conclusion is that the two fractal dimensions are in fact identical the deterministic fractals we study are sierpinski carpets sc in a two dimensional space and the random fractals are percolation clusters at criticality as an intermediate case we present results on some randomized sc in the random structures statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed two different definitions of the borderline are used considering nearest neighbours as well as nearest and second nearest neighbours as connected the conclusion is valid for both cases

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

transparency effects in cluster cluster aggregation with linear trajectories two hierarchical models of cluster cluster aggregation whose aggregates follow random linear trajectories with model i or without model ii random impact parameter are investigated numerically the difference of the fractal dimension d of the clusters as a function of space dimension d is attributed to transparency effects which are less important in model ii a simple argument is given which suggests that in contrast with model i model ii should not have an upper critical dimension

regular random fractals and the n parameter model two models of fractal objects are presented the first model represents a new class of fractals which is intermediate to statistical fractals and exact fractals in that each configuration of the random ensemble has an exact and adjustable fractal dimension the second model has a continuously adjustable backbone dimensions and can be used to directly generate conducting backbones

generating connected textured fractal patterns using markov random fields an algorithm that yields textured and connected binary fractals is presented the texture is imposed by modelling the fractal as a markov random field mrf at every resolution level the model size and the parameters specify the texture the generation starts at a coarser level and continues at finer levels connectivity which is a global property is maintained by restricting the flow of the sample generating markov chain within a limited subset of all possible outcomes of the markov random field the texture is controlled by the parameters of the mrf model being used sample patterns are shown

a monte carlo renormalisation approach to fractal dimensions of infinite cluster backbone and cutting bonds for percolation a monte carlo renormalisation group method is presented to study the cluster structure of an infinite cluster at the percolation threshold applying this technique to bond percolation on the square lattice fractal dimensions of an infinite cluster its backbone and cutting bonds are calculated this method converges very rapidly with an increase in the size of the cell the author estimates that the fractal dimension of an infinite cluster d 1 88 or 0 02 the fractal dimension of its backbone db 1 62 or 0 02 and the fractal dimension of its cutting bonds dc 0 75 or 0 01 up to the scale factor b 10 in excellent agreement with the large cell monte carlo simulation result

comments on on the stability of discrete time sliding mode control systems with reply in the above paper by s z sarpturk and y istefanopulos see ieee trans automat contr vol ac 32 p 930 2 1987 stability conditions for discrete time sliding mode control systems are presented which require the stabilizing control to be upper and lower bounded the present author shows that these bounds depend on the distance of the system state from the sliding manifold and that they converge as the state approaches the manifold sarpturk and istefanopulos agree that the bounds of the discrete time control guaranteeing the stability of the sliding mode system depend also on the distance of the state from the sliding manifold therefore in order to guarantee the stability of the sliding mode system the controls must be chosen so as to satisfy the convergence and sliding bounds derived in the paper

hierarchical model for irreversible kinetic cluster formation a model is proposed to describe the growth of clusters by a mechanism of irreversible clustering of clusters the fractal exponent is extracted by means of numerical simulations on small systems both directly and in the form of a renormalisation group analysis the results are in excellent agreement with previous monte carlo simulations the numerical precision is better due to the simpler hierarchical formulation of the model in the present form the model looks like the diffusion limited aggregation model which for the sake of comparison is treated by the same renormalisation group method

robust strong stabilization via modified popov controller synthesis in this paper the authors merge the parameter dependent lyapunov function framework used to construct robust popov controllers with the a priori and a posteriori approaches for obtaining stable compensators specifically the authors derive constructive sufficient conditions that yield robust lyapunov and asymptotically stable stabilizing popov dynamic compensators

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

particle aggregation versus cluster aggregation in high dimensions we distinguish two different types of irreversible aggregation accretion of individual particles and successive aggregation of clusters of comparable size in aggregation of particles which follow trajectories of fractal dimensiond 1 we show that physical limits on the aggregation rate impose a lower bound on the fractal dimensiond 0 of the aggregate ind dimensional space d 0 d d 1 1 thus aggregation of ballistic particles withd 1 1 is not fractal by contrast cluster aggregates appear to attain a finite limitingd 0 in high dimensions we present a soluble model with this property and argue that it should agree with sutherland s binary aggregation model in high dimensions for this model d 0 depends continuously on a parameter the exponent is not universal

the fractal dimension of cluster perimeters generated by a kinetic walk the fractal dimension dg of cluster perimeters generated by a recently proposed butterfly growth walk is considered in the long range limit of the walk on a percolation cluster dg appears to be equal to the fractal dimension of the singly connected bonds dg 1 nu the new relation for chemical dimension dl is proposed dl df df dg in the short range limit the butterfly walk on a euclidean lattice appears to be in the same universality class as a random walk the dynamic aspect of the growth walk is discussed and the continuously tunable spectral dimension is obtained both short and long range limits of this diffusion process are different from a random diffusion on percolation

a new texture generation method based on pseudo dct coefficients in this paper a new method for generating different texture images is presented this method involves a simple transform from a certain one dimensional 1 d signal to an expected two dimensional 2 d image unlike traditional methods the input signal is generated by a simple 1 d function in our work instead of a sample texture we first transform the 1 d input signal into frequency domain using fast fourier transform based on the sufficient analysis in 2 d discrete cosine transform dct domain where each of the coefficients expresses a texture feature in a certain direction the 2 d pseudo dct coefficients are then constructed by appropriately rearranging the fourier coefficients in terms of their frequency components finally the corresponding texture image can be produced by 2 d inverse dct algorithm we applied the proposed method to generate several stochastic textures i e cloud illumination and sand and several structural texture images experimental results indicate the good performance of the proposed method

exact semi internal control of an euler bernoulli equation this paper proves exact semi internal controllability of an euler bernoulli equation with variable coefficients the basic principle of the proof is the hilbert uniqueness method for this a multiplier technique and a unique continuation property have been used the proof of the unique continuation property is the main feature of this work