variable delay feedback control of unstable steady states in retarded time delayed systems we study the stability of unstable steady states in scalar retarded time delayed systems subjected to a variable delay feedback control the important aspect of such a control problem is that time delayed systems are already infinite dimensional before the delayed feedback control is turned on when the frequency of the modulation is large compared to the system s dynamics the analytic approach consists of relating the stability properties of the resulting variable delay system with those of an analogous distributed delay system otherwise the stability domains are obtained by a numerical integration of the linearized variable delay system the analysis shows that the control domains are significantly larger than those in the usual time delayed feedback control and that the complexity of the domain structure depends on the form and the frequency of the delay modulation

the liapunov dimension of strange attractors abstract many papers have been published recently on studies of dynamical processes in which the attracting sets appear quite strange in this paper the question of estimating the dimension of the attractor is addressed while more general conjectures are made here particular attention is paid to the idea that if the jacobian determinant of a map is greater than one and a ball is mapped into itself then generically the attractor will have positive two dimensional measure and most of this paper is devoted to presenting cases with such jacobians for which the attractors are proved to have non empty interior

long range order in the scaling behaviour of hyperbolic dynamical systems abstract detailed statistical analyses of chaotic signals have been so far limited to 2 d maps with one expanding and one contracting direction here by studying filtered signals we provide evidence that the existence of a further stable direction can transform self similarity into self affinity and generate phase transitions according to the thermodynamic formalism of dynamical systems in a hyperbolic case the dimension spectrum is computed exactly as a function of the filter cut off frequency moreover the validity of the kaplan yorke formula and of its generalization are rigorously proven finally the scaling function is shown to satisfy a stochastic recursive relation whose lyapunov exponent allows to control the extension of the range of interactions in the associated hamiltonian

exact enumeration approach to fractal properties of the percolation backbone and 1 σ expansion an exact numeration approach is developed for the backbone fractal of the incipient infinite cluster at the percolation threshold the authors use this approach to calculate exactly the first low density expansion of lbb p for arbitrary system dimensionality d where lbb p is the mean of backbone bonds and p is the bond occupation probability standard series extrapolation methods provide estimates of the fractal dimension of the backbone for all d these disagree with the sierpinski gasket model of the backbone they also calculate the first low density expansions of lmin p and lred p which are respectively the mean number of bonds in the minimum path between i and j and the mean number of singly connected red bonds

a design theory for solving the anomalies problem a theory is proposed for designing database schemes that are free of update anomalies unlike previous approaches insertion and deletion anomalies are investigated in the context of a relation scheme while replacement anomalies are studied in the context of a database scheme two simple models are developed for analyzing when a relation scheme is free of insertion and deletion anomalies techniques are also proposed for obtaining desirable decompositions that are free of insertion and deletion anomalies a class of database schemes that is free of replacement anomalies is also proposed this class of schemes is highly desirable with respect to constraint enforcement when attribute values of some tuple are being changed by making different assumptions on the modifiable attributes several important classes of database schemes that are free of replacement anomalies are characterized throughout we assume update operations are performed on relation schemes at the conceptual level

counterexample to some shape equations for axisymmetrical vesicles three different shape equations for axisymmetric vesicles have been derived from the same spontaneous curvature model in literature the validity of the equations has been examined by means of a rigorous analytical solution for axisymmetric vesicles a counterexample is given to show the invalidity of two of the equations

insertion anomalies and the justification for 4nf in relational databases abstract the issue of providing a formal justification for the use of fourth normal form 4nf in relational database design is investigated extending earlier work by other authors that provided formal definitions of an insertion anomaly in the case of functional dependency fd constraints formal definitions are provided for two types of an insertion anomaly for the case when both fd and multivalued dependency mvd constraints are permitted it is shown that both types of insertion anomaly are equivalent conditions on a relation scheme and a relation scheme is in 4nf if and only if both anomalies are absent it is also shown that another type of insertion anomaly that does not reflect the symmetrical nature of mvds is a weaker condition than 4nf

invasion percolation new algorithms and universality classes employing highly efficient algorithms for simulating invasion percolation ip whose execution time scales as o mlog m or better for a cluster of m sites and for determining the backbone of the cluster we obtain precise estimates for the fractal dimensions of the sample spanning cluster the backbone and the minimal path in order to identify the universality classes of four different ip processes site and bond ip with and without trapping in two dimensions ip is characterized by two universality classes one each for ip without trapping and site and bond ip with trapping in a three dimensional site ip with and without trapping is in the universality class of random percolation while bond ip with trapping is in a distinct universality class which may be the same as that of optimal paths in strongly disordered media

multifractality and the kauffman model the author simulates the spread of an initial damage in the kauffman cellular automata at its critical point on the square lattice he calculates various moments of the probability that a site has been damaged n times and checks for multifractality in the critical exponents for different ensembles specifically he finds no evidence for multifractality when the moments of the probabilities are evaluated with lattice size l but multifractal behaviour occurs when the moments are monitored as a function of time t

vanishing gaps in 1d bandstructures the criterion for vanishing or zero energy gaps in the spectrum of 1d electronic bandstructures is obtained from perturbation theory it is in agreement with examples of periodic potentials which never exhibit zero gaps as well as with those which may including certain smooth periodic potentials the results have relevance to recent work in the field of semiconductor layered heterostructures or superlattices the analysis should also have implications for other problems that involve hill s determinant

five turbulent problems abstract five questions which involve strange attractors in one way or another are discussed these are the choice of probability measures to describe turbulence the hausdorff dimension of julia sets for rational maps of the riemann sphere the existence of nonperiodic turbulent crystal structure the mechanism generating intermittency in developed hydrodynamic turbulence the distribution of characteristic exponents in a turbulent fluid

inverted catenoid as a fluid membrane with two points pulled together under inversion in any interior point a catenoid transforms into a deflated compact geometry which touches at two points its poles the catenoid is a minimal surface and as such is an equilibrium shape of a symmetric fluid membrane the conformal symmetry of the hamiltonian implies that inverted minimal surfaces are also equilibrium shapes however they will exhibit curvature singularities at their poles such singularities are the geometrical signature of the external forces required to pull the poles together these forces will set up stresses in the inverted shapes tuning the force corresponds geometrically to the translation of the point of inversion for any fixed surface area there will be a maximum force the associated shape is a symmetric discocyte lowering the external force will induce a transition from the discocyte to a cup shaped stomatocyte

some relations between dimension and lyapounov exponents we consider differentiable maps and compact invariant sets we introduce dimensional quantities related to the ergodic invariant measures and prove some simple relations

conductivity exponent and backbone dimension in 2 d percolation abstract we present high statistics simulations for 2 d percolation clusters in the bus bar geometry at the critical point for site and for bond percolation we measured their backbone sizes and electrical conductivities for all sets of measurements we find large corrections to scaling most of which do not seem to be described by single powers using single power terms for the corrections to scaling of the backbone masses we would obtain fractal dimensions which are different for site and bond percolation while the correct result is d b 1 6432 0 0008 for both for the conductivity the corrections to scaling are strongly non monotonic for bond percolation the exponent t t is measured as 0 9826 0 0008 in disagreement with the alexander orbach and other conjectures

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

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

properties of border states of transient chaos transient chaos with absolutely continuous conditionally invariant measure is studied and a general solution of the frobenius perron equation is presented for complete one dimensional maps in particular properties of borderline situations exhibiting phase transitions within the framework of thermodynamical formalism are investigated

bifurcation and chaotic motion of a soliton in a long josephson junction oscillator the fluxon dynamics of a long josephson junction ljj is investigated numerically the effect of the surface resistance of the superconductor on the bifurcation phenomenon is examined in detail we show the occurrence of a period doubling route to chaos and the reappearance of low order periodic motions in the ljj by varying the magnitude of the external force the chaotic attractors of the ljj are characterized using maximal lyapunov exponents and a fractal correlation dimension we show the existence of noise induced oscillations in a force free ljj system finally the influence of noise on the periodic and chaotic dynamics is also presented

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

singular value decomposition in attractor reconstruction pitfalls and precautions applicability of singular value decomposition for reconstructing the strange attractor from one dimensional chaotic time series proposed by broomhead and king is extensively tested and discussed previously published doubts about its reliability are confirmed singular value decomposition by nature a linear method can bring distorted and misleading results when nonlinear structures are studied

numerical observation of nonaxisymmetric vesicles in fluid membranes by means of surface evolver a software package of brute force energy minimization over a triangulated surface developed by the geometry center of the university of minnesota exp math 1 141 1992 we have numerically searched the nonaxisymmetric shapes under the helfrich spontaneous curvature sc energy model we show that there are abundant mechanically stable nonaxisymmetric vesicles in the sc model including both regular shapes with intrinsic geometric symmetry and complex irregular ones we report in this paper a catalog of interesting shapes including a corniculate shape with six corns a quadriconcave shape a shape resembling sickle cells a shape resembling acanthocytes and two tubelike shapes most of these shapes can be related to experimental observations in red blood cells and other experiments in fluid membrane s1063 651x 98 06510 6

a precise characterization of three dimensional percolating backbones the backbones of three dimensional critical percolation clusters are extracted and the fractal dimension is accurately calculated using various mass scaling and box counting techniques to be dfb 1 855 or 0 015 the eigenvalue spectrum of the brownian transition probability matrix is studied numerically which results in the estimates dwb 3 13 or 0 03 for the walk dimension and dsb 1 18 or 0 01 for the spectral dimension of the backbone independent calculation of all three quantities allows the conductivity exponent mu to be determined and also allows the validity of the scaling relation ds 2df dw proposed by alexander and orbach 1982 to be tested on the backbone

numerical studies of critical percolation in three dimensions presents results of high statistics simulations of the spreading of 3d percolation close to the critical point the main results are i a more precise estimate of the spreading resp chemical distance dimension ii a novel heuristic scaling theory for percolation near surfaces and iii more precise values for critical surface and edge exponents in addition the author verifies the very precise results of ziff and stell 1988 for the percolation thresholds and studies in detail corrections to scaling the latter is made possible by simulating bond and site percolation in a number of different geometries in addition in most cases one could measure more than one observable during each simulation which provided quite severe internal consistency constraints in some cases the author found quite important deviations from scaling which are not easily described by a single power or logarithmic correction term

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

classical diffusion on eden trees we study an aggregation process which gives rise to compact clusters with no loops a generalization of the node counting theorem applicable to such branched graphs trees is proved this is used to determine the spectral dimension of these clusters on square and cubic embedding lattices by monte carlo simulations the results are explained in terms of the geometric structure of these trees

corrections to scaling for diffusion exponents on three dimensional percolation systems at criticality recent results of monte carlo simulations of the ant in the labyrinth method in three dimensional percolation lattices are reanalyzed in the light of more accurate corrections to scaling ansatz motivated by inconsistent results that have appeared in the literature the results are observed to be sensitive to the form of the scaling correction terms using a single correction term we estimate the valuek 0 197 0 004 for the anomalous diffusion exponent at criticality when two correction terms are included k 0 200 0 002 is obtained these new estimates are consistent with known theoretical bounds with recent series expansion results and with numerical calculations of the conductance of random resistor networks above criticality

a geometric theory on the elasticity of bio membranes the purpose of this paper is to study the shapes and stabilities of bio membranes within the framework of exterior differential forms after a brief review of the current status of theoretical and experimental studies on the shapes of bio membranes a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers the shape equation and boundary conditions of open lipid bilayers and two component membranes the shape equation and in plane strain equations of cell membranes with cross linking structures and the stabilities of closed lipid bilayers and cell membranes the key point of this scheme is to deal with the variational problems on surfaces embedded in three dimensional euclidean space by using exterior differential forms

axiomatisations of functional dependencies in the presence of records lists sets and multisets we investigate functional dependencies in databases that support complex values such as records lists sets anu multisets therefore an abstract algebraic framework is proposed that classifies data models according to the underlying types they support this allows to emphasise the impact of the data types rather than the specifics of a particular data model the main results are finite minimal sound and complete sets of inference rules for the implication of functional dependencies in the presence of records and all combinations of lists sets and multisets the inference rules are similar to armstrong s original axioms for the relational data model thanks to the algebraic framework the completeness result however requires a deep analysis in the case of sets and in particular multisets

a precise determination of the backbone fractal dimension on two dimensional percolation clusters the backbone fractal dimension dbf is calculated on two dimensional percolation clusters at the percolation threshold studies are carried out on backbones defined in three different ways bus bar point to point and with fully periodic boundaries the estimates of dbf are obtained by measuring the variation of mass with radius for all clusters and by means of finite size scaling on the bus bar backbones all cases imply a value of dbf 1 64 or 0 01 for the backbone fractal dimension because of the high degree of self consistency of all the results the authors believe that this estimate represents a considerably improved accuracy

analysis on an ode arisen from studying the shape of a red blood cell we study the existence problem of a special solution to the helfrich functional such that it corresponds to a surface of the shape of a red blood cell the helfrich functional is also a perturbation of the willmore functional involving some parameters with physical meanings with the expected symmetry of the surface it reduces to an analysis on an ode with certain shape requirements we discover a sufficient condition on the parameters which ensures the existence of such a special solution to the ode

rational dynamical zeta functions for birational transformations we propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables depending on two parameters this conjectured function is a simple rational expression with integer coecients this yields an algebraic value for the topological entropy furthermore the generating function for the arnold complexity is also conjectured to be a rational expression with integer coecients with the same singularities as for the dynamical zeta function this leads at least in this example to an equality between the asymptotic of the arnold complexity and the exponential of the topological entropy we also give a semi numerical method to eectively compute the arnold complexity c 1999 published by elsevier science b v all rights reserved

diffusion and spectral dimension on eden tree the authors calculate the eigenspectrum of random walks on the eden tree in two and three dimensions from this they calculate the spectral dimension ds and the walk dimension dw and test the scaling relation ds 2df dw 2d dw for an eden tree finite size induced crossovers are observed whereby the system crosses over from a short time regime where this relation is violated particularly in two dimensions to a long time regime where the behaviour appears to be complicated and dependent on dimension even qualitatively

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

shape equations of the axisymmetric vesicles based on the same bending energy of the spontaneous curvature model three shape equations for axisymmetric vesicles are derived from different variational methods they are degenerate for the spherical vesicle while for the cylindrical vesicle two of them are the same they all have a special toroidal solution clifford tori but the constraints on the lagrange multipliers deltap and lambda and the spontaneous curvature c0 are different we consider the physical mode of variation and introduce an arbitrary parameter for the axisymmetric action we get the shape equation in terms of this parameter from it when this parameter is identified as the parameter rho it reduces to the same equation that is from the general shape equation

on the control of complex dynamic systems a method is described for the limited control of the dynamics of systems which generally have several dynamic attractors associated either with maps or first order ordinary differential equations ode in rn the control is based on the existence of convergent regions cc k 1 2 in the phase space of such systems where there is local convergence of all nearby orbits the character of the control involves the entrainment and subsequent possible migration of the experimental system from one attractor to another entrainment means that limt x t g t 0 where x t rn is the system s controlled dynamics and the goal dynamics g t gk has any topological form but is limited dynamically and to regions of phase space gk contained in some ck gk ck the control process is initiated only when the system enters a basin of entrainment bek gk associated with the goal region gk aside from this macroscopic initial state information about the system no further feedback of dynamic information concerning the response of the system is required the experimental reliability of the control requires that the regions bek be convex regions in the phase space which can apparently be assured if gk ck simple illustrations of these concepts are given using a general linear and a piecewise linear ode in rn in addition to these entrainment goals migration goal dynamics is introduced which intersects two convergent regions g cj g cj i j and permits transferring the dynamics of a system from one attractor to another or from one convergent region to another in the present study these concepts are illustrated with various one dimensional maps involving one or more attractors and convergent regions several theorems concerning entrainment are derived for very general continuous one dimensional maps sufficient conditions are also established which ensure near entrainment for a system when the dynamic model of the system is not exactly known the applications of these concepts to higher dimensional maps and flows will be presented in subsequent studies

on the metric properties of the feigenbaum attractor the two standard literature definitions of the function associated with the feigenbaum attractor are not equivalent the method due to vulet al and feigenbaum is used to calculate the haussdorff dimension of the feigenbaum attractor using as input the trajectory scaling functions the two calculations yield the same hausdorff dimensiond 0 5380451435 to within the accuracy of the computation

evaluation of probabilistic and dynamical invariants from finite symbolic substrings comparison between two approaches abstract while evaluating scaling functions of fractal dimensions and lyapunov exponents from time series in the traditional way assumptions are made concerning the grammar of the underlying dynamical system it is implicitly assumed that the length of the substrings considered is sufficient to capture the grammatical properties of the system in this contribution we show where this assumption becomes relevant we give an example of a simple grammatical rule which leads to badly behaving convergence properties of the associated scaling functions as another consequence of our investigations we conclude that whenever a finite grammar is encountered the cycle expansion approach of cvitanovic using periodic orbits should preferably be used

determination of fractal dimensions for geometrical multifractals abstract two independent approaches the box counting and the sand box methods are used for the determination of the generalized dimensions d q associated with the geometrical structure of growing deterministic fractals we find that the multifractal nature of the geometry results in an unusually slow convergence of the numerically calculated d q s to their true values our study demonstrates that the above mentioned two methods are equivalent only if the sand box method is applied with an averaging over randomly selected centres in this case the latter approach provides better estimates of the generalized dimensions

spheres and prolate and oblate ellipsoids from an analytical solution of the spontaneous curvature fluid membrane model an analytic solution for the helfrich spontaneous curvature membrane model h naito m okuda and pu yang zhong can phys rev e 48 2304 1993 54 2816 1996 which has the conspicuous feature of representing a circular biconcave shape is studied results show that the solution in fact describes a family of shapes which can be classified as i a flat plane trivial case ii a sphere iii a prolate ellipsoid iv a capped cylinder v an oblate ellipsoid vi a circular biconcave shape vii a self intersecting inverted circular biconcave shape and viii a self intersecting nodoidlike cylinder among the closed shapes ii vii a circular biconcave shape is the one with a minimum of local curvature energy s1063 651x 49 00309 8

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed