geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices it is claimed that the abstract analytic continuation of hypercubic lattices to noninteger dimensionalities can be implemented explicitly by certain fractal lattices of low lacunarity these lattices are special examples of sierpinski carpets their being of low lacunarity means that they are arbitrarily close to being translationally invariant the claim is substantiated for the ising model in d 1 ensuremath epsilon dimensions and for resistor network models with 1ldl2

lacunarity and multifractal analysis of the large dla mass distribution abstract we show the methodology used to analyze fractal and mass multifractal properties of very large diffusion limited aggregation dla clusters with a maximum of 10 9 particles for 2d aggregates and 10 8 particles for 3d clusters to support our main result the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects in order to estimate lacunarity measures for large dla clusters we develop a variant of the gliding box algorithm which reduces the computer time needed to obtain experimental results we show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters lacunarity analysis shows provided we study small clusters mass distributions data which might be interpreted as two different values of fractal dimensions while the cluster grows however this effect tends to vanish when the cluster size increases further in such a way that monofractality is achieved the outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior vicsek et al 1990 13 detected for dla clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena since the scaling behavior of our dla clusters space corresponds to monofractal objects being this situation remarkably noticeable in the limit of very large clusters

a renorming in some banach spaces with applications to fixed point theory abstract we consider a banach space x endowed with a linear topology and a family of seminorms r k which satisfy some special conditions we define an equivalent norm on x such that if c is a convex bounded closed subset of x which is relatively sequentially compact then every nonexpansive mapping t c c has a fixed point as a consequence we prove that if g is a separable compact group its fourier stieltjes algebra b g can be renormed to satisfy the fpp in case that g t we recover p k lin s renorming in the sequence space l 1 moreover we give new norms in l 1 with the fpp we find new classes of nonreflexive banach spaces with the fpp and we give a sufficient condition so that a nonreflexive subspace of l 1 can be renormed to have the fpp

on the yang lee edge singularity for ising model on nonhomogeneous structures abstract we studied distribution of zeros of the partition function of ferromagnetic ising model near the yang lee edge on two self similar structures we have shown that the nature of associated critical behavior crucially depends on the local lattice structure if the sites of higher coordination number make an infinite connected cluster then we find an usual power law behavior while a logarithmic divergence of the correlation length develops near the edge in the case that these sites make only finite islands we reveal also a close connection between yang lee edge critical behavior and critical behavior of a simple zero field gaussian model on the same structures

bose like oscillator in fractional dimensional space the system of a fractional dimensional bose like oscillator of one degree of freedom whose canonical variables satisfy the general wigner commutation relations is investigated momentum position uncertainty relations are obtained for states without definite parity the well known one dimensional heisenberg uncertainty principle is retained but for odd and even states momentum position uncertainty inequalities depending on the dimension of the space are obtained the motions of both the free particle and the harmonic oscillator in a fractional dimensional space are studied through the probability density function the existence of compression spread of the probability density for dimensions d 1 is shown fractional dimensional bose like operators are also deduced they together with the reflection operator form an r deformed heisenberg algebra with a deformation parameter depending on the dimension of the space

spectral dimension of a wire network by a rigorous analysis for diffusion on a wire network the spectral dimension of a fractal is shown to be independent of the local structure it is discussed that diffusion does not occur when the lattice spacing tends to zero on such a fractal that the spectral dimension is less than the hausdorff dimension if a free field on the fractal exhibits a certain long distance behaviour for a sierpinski carpet the spectral dimension is evaluated within bond moving approximation migdal kadanov renormalisation as a result the author obtains a value smaller than the hausdorff dimension

some fixed point results on l embedded banach spaces abstract in this paper we prove that w fixed point property and w fixed point property are equivalent concepts for l embedded banach spaces which are duals of m embedded spaces similar results will be obtained with respect to the normal structure these equivalences will be applied to establish new fixed point results for different examples we will also prove the existence of fixed points for both nonexpansive and asymptotically regular mappings defined on subsets of l embedded banach spaces which are sequentially compact for the abstract measure topology we will check that our results do not hold in the case of the weak topology

relationship of second order lacunarity hurst exponent brownian motion and pattern organization abstract second order lacunarity metrics are related to the hurst exponent h fractional brownian motion with h 0 5 is used as a benchmark for quantifying patterns local versus global correlation and implications for pattern organization are discussed

spaces of compact operators on a hilbert space with the fixed point property abstract every non reflexive subspace of k h the space of compact operators on a hilbert space h contains an asymptotically isometric copy of c 0 this along with a result of besbes shows that a subspace of k h has the fixed point property if and only if it is reflexive

statistical analysis of digital images of periodic fibrous structures using generalized hurst exponent distributions abstract distinction of diverse two dimensional periodic structures can be based on a large number of methods and parameters while the quantitative description of differences between similar samples is usually difficult this article aims by the use of statistical random walk in a generalized q order dimensional space at introducing a methodology to qualify the networked structures on the basis of exemplary textile samples the presented results were obtained at 1 bit monochromatic maps obtained from optical microscopic pictures significant features of samples were represented by the obtained distributions of hurst exponents and shannon entropy calculations

fourier stieltjes algebras and measure algebras on compact right topological groups abstract let g be an admissible compact hausdorff right topological group that is a group with a hausdorff topology such that for each a g the map g g a is continuous and the set of a g such that the map g a g is continuous is dense in g such groups arise in the study of distal flows in this paper we study the fourier stieltjes algebra b g the linear span of the continuous positive definite functions on g we show that b g is isomorphic with the fourier stieltjes algebra of an associated compact topological group this result is then applied to obtain some geometric properties including the weak and weak fixed point properties on b g we also study some related properties on the measure algebra m g

isometric copies of c0 and l in duals of banach spaces abstract let x be a banach space then x contains an isometric copy of l if and only if x contains an asymptotically isometric copy of c0

weight restrictions and free production in data envelopment analysis it is known that the incorporation of weight restrictions in models of data envelopment analysis may result in their infeasibility in our paper we investigate this effect in detail we show that the infeasibility is only one of several possible outcomes that point to a particular problem with weight restrictions for example the use of weight restrictions may also lead to zero or negative efficiency scores of some units removing problematic units from the data set does not necessarily remove the underlying problem caused by the weight restrictions and only makes it undetected we prove that all such problems arise when weight restrictions induce free or unlimited production of outputs in the underlying technology this is unacceptable from the production theory point of view and indicates that the weight restrictions need reassessing we develop analytical criteria and computational methods that allow us to identify the above problematic situations

renormings and the fixed point property in non commutative l1 spaces abstract let m be a finite von neumann algebra it is known that l 1 m and every non reflexive subspace of l 1 m fail to have the fixed point property for non expansive mappings fpp we prove a new fixed point theorem for this class of mappings in non commutative l 1 m banach spaces which lets us obtain a sufficient condition such that a closed subspace of l 1 m can be renormed to satisfy the fpp as a consequence we deduce that the predual of every atomic finite von neumann algebra can be renormed with the fpp

phase transitions for polymers on fractal lattices abstract models of linear and branched polymers on finitely ramified fractal lattices are briefly reviewed their foremost interest is to provide exactly solvable systems with phase transitions at finite values of the fugacity or temperature this gives insight into the behaviour of polymers in inhomogeneous media their collapse transition and their adsorption at surfaces some unexpected results are also found such as the possible existence of essential singularities in generating functions or the non convergence of critical exponents towards their eucledean limit

there is an equivalent norm on l1 that has the fixed point property abstract let k 8 k 1 8 k for all k n and let be the equivalent norm of l 1 defined by a n sup k n k n k a n for all x a n l 1 we prove that l 1 has the fixed point property for nonexpansive self mappings

lacunarity and universality lacunarity as a criterion of universality in phase transitions on sierpinski carpets is studied the approximate theoretical and numerical results suggest that systems of different lacunarity may belong to a common universality class there seems to be a lack of solutions to the complete set of universality criteria on sierpinski carpets

failure of the fpp inside an asymptotically isometric free copy of c0 abstract we produce an equivalent renorming of c 0 which fails to contain an asymptotically isometric copy of c 0 yet all of its infinite dimensional subspaces fail to have the fixed point property for nonexpansive mappings on closed bounded convex subsets

order asymptotically isometric copies of l l1 and c0 in banach function spaces abstract we investigate order asymptotically isometric copies of c 0 l and l 1 in kothe spaces firstly we prove a number of general relations between them and we discuss what happens with such copies while passing to kothe dual spaces or vice versa passing to preduals finally we apply the results to characterize certain classes of kothe spaces as orlicz spaces calderon lozanovski spaces orlicz lorentz spaces and musielak orlicz spaces with such copies

influence of image resolution and evaluation algorithm on estimates of the lacunarity of porous media in recent years experience has demonstrated that the classical fractal dimensions are not sufficient to describe uniquely the interstitial geometry of porous media at least one additional index or dimension is necessary lacunarity a measure of the degree to which a data set is translationally invariant is a possible candidate unfortunately several approaches exist to evaluate it on the basis of binary images of the object under study and it is unclear to what extent the lacunarity estimates that these methods produce are dependent on the resolution of the images used in the present work the gliding box algorithm of allain and cloitre phys rev a 44 3552 1991 and two variants of the sandbox algorithm of chappard et al j pathol 195 515 2001 along with three additional algorithms are used to evaluate the lacunarity of images of a textbook fractal the sierpinski carpet of scanning electron micrographs of a thin section of a european soil and of light transmission photographs of a togolese soil the results suggest that lacunarity estimates as well as the ranking of the three tested systems according to their lacunarity are affected strongly by the algorithm used by the resolution of the images to which these algorithms are applied and at least for three of the algorithms producing scale dependent lacunarity estimates by the scale at which the images are observed depending on the conditions under which the estimation of the lacunarity is carried out lacunarity values range from 1 02 to 2 14 for the three systems tested and all three of the systems used can be viewed alternatively as the most or the least lacunar some of this indeterminacy and dependence on image resolution is alleviated in the averaged lacunarity estimates yielded by chappard et al s algorithm further research will be needed to determine if these lacunarity estimates allow an improved unique characterization of porous media

asymptotically isometric copies ofc0in banach spaces abstract if is an uncountable set then any equivalent renorming of c 0 contains an asymptotically isometric copy of c 0 if y is an infinite dimensional closed subspace of c 0 then y contains an asymptotically isometric copy of c 0 if x and y are two infinite dimensional banach spaces and if x contains an asymptotically isometric copy of c 0 then the injective tensor product of x and y x e y contains a complemented asymptotically isometric copy of c 0 similarly if x contains an asymptotically isometric copy of c 0 then the lebesgue bochner space l p 0 1 x contains a complemented asymptotically isometric copy of c 0

potts model on sierpinski carpets and their relation to hypercubic lattices of non integer dimensionality the authors study the critical frontiers and the high and low temperature asymptotic behavior of the potts model two site correlation function for several sierpinski carpets with fractal dimension lying between one and two they simulate the sierpinski carpets by means of appropriate hierarchical lattices obtaining from their basic cells the two graphs among others that arise from the anisotropic bond moving schemes they correspond to the asymptotic high and low temperature dominant terms for the hierarchical lattice two site correlation function exact result by taking the infinite limit size of the basic cell these asymptotic behaviors tends to those of the sierpinski carpets it is then possible to compare them with similar results obtained from analytical extension to d 2 of the hypercubic lattice their results indicate that these asymptotic behaviors do not always coincide suggesting that possibly they may not identify the sierpinski carpets exhibited by gefen et al 1984 as a correct implementation of the analytical extension of hypercubic lattices

identification of congestion in data envelopment analysis under the occurrence of multiple projections a reliable method capable of dealing with negative data abstract to detect the weak and strong congestion statuses of decision making units dmus via data envelopment analysis dea first a technology is constructed under the assumptions of convexity and strong output disposability then the congestion of any inefficient dmu is defined at its projection on the efficient frontier of this technology it has however been argued that this definition is not precise under the occurrence of multiple projections in this paper therefore we propose a single stage linear programming lp model to recognize the evidence of congestion our model precisely distinguishes between the dmus exhibiting weak but not strong congestion and those suffering from strong congestion and identifies the full efficient dmus as well to cope effectively with the occurrence of multiple projections we first prove that all relative interior points of a face exhibit the same type of congestion based on this finding we define the congestion of an inefficient dmu at its max projection a projection that lies in the relative interior of the corresponding minimum face then by showing that the global reference set spans the minimum face we propose an lp model for identifying the max projection we highlight a theoretically interesting and practically useful consequence of our results that the congestion status of an inefficient dmu can be determined based on those of its reference dmus furthermore our proposed method can deal with negative data and is also computationally more efficient than the existing approaches finally three numerical examples are presented to illustrate the use of our proposed method

renormings and fixed point property in non commutative l1 spaces ii affine mappings abstract in this paper we prove that every noncommutative l 1 space associated to a finite von neumann algebra can be renormed to satisfy the fixed point property for nonexpansive affine mappings particular examples are l 1 r where r is the hyperfinite i i 1 factor and the function spaces l 1 0 1 and l 1 for any finite measure space this property does not hold for the usual 1 norm

phase transitions on fractals iii infinitely ramified lattices for pt ii see ibid vol 17 p 435 1984 in the first two papers of this series the authors considered self similar fractal lattices with a finite order of ramification r in the present paper they study physical models defined on a family of fractals with r infinity in order to characterise the geometry of these systems they need the connectivity q and the lacunarity l in addition to the fractal dimensionality d it is found that discrete symmetry spin models on these lattices undergo a phase transition at tc 0 an approximate renormalisation group scheme is constructed and used to find the dependence of tc and the critical exponents on the geometrical factors they also solve the problem of resistor networks on these fractals and discuss its consequences concerning spin models with continuous symmetry

renormings of c0 and the fixed point property it is unknown whether all renormings of c0 fail the fixed point property fpp or not in this note we give a sufficient condition for a renorming of c0 to fail the fpp which is more general than the previously known ones in fact the condition is satisfied for all renormings of c0 we know it also allows us to show that for some usual renormings of c0 not only the whole space but all its infinite dimensional subspaces fail the fpp

decomposable multiphase entropic descriptor abstract to quantify the degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor ed of a pillar model developed to greyscale images to uncover the contribution of each phase we introduce the suitable phase splitting of the adapted descriptor as a result each of the phase descriptors pds describes the spatial inhomogeneity attributed to each phase component obviously their sum equals the value of the overall spatial inhomogeneity we apply this approach to three phase synthetic patterns the black and grey components are aggregated or clustered while the white phase is the background one the examples show how the valuable microstuctural information related separately to each of the phases can be obtained at any integer length scale even dissimilar hidden statistical periodicities can be easily detected for chosen phases built up of compact regular clusters

solving dea models in a single optimization stage can the non archimedean infinitesimal be replaced by a small finite epsilon abstract single stage dea models aim to assess the input or output radial efficiency of a decision making unit and potential mix inefficiency in a single optimization stage this is achieved by incorporating the sum of input and output slacks multiplied by a small theoretically non archimedean infinitesimal value epsilon in the envelopment model or equivalently by using this value as the lower bound on the input and output weights in the dual multiplier model when this approach is used it is common practice to select a very small value for epsilon this is based on the expectation that for a sufficiently small epsilon the radial efficiency and optimal slacks obtained by solving the single stage model should be approximately equal to their true values obtained by the two separate optimization stages however as well known selecting a small epsilon may lead to significant computational inaccuracies in this paper we prove that there exists a threshold value referred to as the effective bound such that if epsilon is smaller than this bound the solution to the single stage program is not approximate but precise exactly the same as in the two stage approach provided there are no computational errors

exact renormalization group approach to critical phenomena in an ising system with long range interactions on the sierpinski gasket lattice abstract an ising spin system with two point long range interactions on the sierpinski gasket lattice is considered the interactions are assigned along edges of all equilateral triangles being part of the self similar structure in addition the long range couplings i e all couplings besides nearest neighbor interactions k are assumed to be independent of the distance i e q1 q l 1 2 where q1 denotes an interaction between the two spins on the distance 2 a with a being a lattice constant and q a positive parameter using an exact renormalization group method based upon the decimation transformation the system is shown to display a line of nontrivial fixed points k k q each point of this line corresponds to a phase transition of a rather high order the critical behavior of the system near every nontrivial fixed point is claimed to be characterized by two dimensions viz the fractal dimension and the so called critical dimension which reflects some topological properties of the system the critical dimension is defined through considering the decay of an effective two point correlation function and depends on q

reflexivity and the fixed point property for nonexpansive maps abstract connections between reflexivity and the fixed point property for nonexpansive self mappings of nonempty closed bounded convex subsets of a banach space are investigated in particular it is shown that l 1 for uncountable sets and l cannot even be renormed to have the fixed point property as a consequence if an orlicz space on a finite measure space that is not purely atomic is endowed with the orlicz norm the orlicz space has the fixed point property exactly when it is reflexive

quantum field theory models on fractal spacetime continuing the analysis of a previous paper the present work applies rigorous renormalization group methods to the hierarchical models to establish the existence of field theories with non gaussian ultraviolet renormalization group fixed points in 4 e dimensions

fractals their transfer matrices and their eigen dimensional sequences this paper defines and studies a general algorithm for constructing new families of fractals in euclidean space this algorithm involves a sequence of linear interscale transformations that proceed from large to small scales the authors find that the fractals obtained in this fashion decompose in intrinsic fashion into linear combinations of a variable number of addend fractals the addends relative weights and fractal dimensionalities are obtained explicitly through an interscale matrix which they call the transfer matrix of the fractal tmf the authors first demonstrate by a series of examples then prove rigorously that the eigenvalues of our tmfs are real and positive and that the fractal dimensions of the addend fractals are the logarithms of the eigenvalues of their tmf they say that these dimensions form the overall fractal s eigendimensional sequence the eigenvalues of their tmf are integers in the non random variants of the construction but are non integer in the random variants a geometrical interpretation of the eigenvalues and the eigenvectors is given their tmf have other striking and very special properties that deserve additional attention

phase transitions on fractals ii sierpinski gaskets for pt i see ibid vol 16 p 1267 1983 the authors construct and investigate a family of fractals which are generalisations of the sierpinski gaskets sgs to all euclidean dimensionalities these fractal lattices have a finite order of ramification and can be considered marginal between one dimensional and higher dimensional geometries physical models defined on them are exactly solvable the authors argue that short range spin models on the sg show no finite temperature phase transitions as examples they solve a few spin models and study the resistor network and percolation problems on these lattices

dilute ising model on fractal lattices the authors study dilute ising models on a family of infinitely ramified exact fractals whose fractal dimension varies from 1 to 2 they calculate the phase diagram and critical exponents as a function of the fractal dimensionality within migdal s approximation 1975

magnetization of a potts ferromagnet on a sierpinski carpet the authors study the inhomogeneous magnetization behaviour of a q state potts ferromagnet on a sierpinski carpet as a function of the temperature using a real space renormalization group procedure two qualitatively different regions on the carpet are distinguished a the interior of the carpet and b the set of internal walls which border the eliminated areas the spontaneous mean magnetization curves for these regions are obtained with the corresponding critical exponents beta and beta w for different values of q they find that the magnetization of region b goes to zero at the critical temperature always below the one of region a

the overall assurance interval for the non archimedean epsilon in dea models a partition base algorithm this study presents an algorithm for determining overall assurance interval of epsilon in dea models in the previous studies in this regard solving n linear programs are needed for this propose where n is the number of decision making units dmu involved in the evaluation this paper based on a classification of dmu s proposes a partition base algorithm that can determine the overall assurance interval of epsilon by solving a few number of linear programs the proposed algorithm is illustrated by the 44 unit data set of power plant systems of iran

fractal dimensionality of polymer chains the authors suggest that the concept of fractal dimensionality provides a useful characterisation of the configurational properties of a single polymer from numerical studies of long polymers traced out by self avoiding walks on a planar lattice they find that the fractal dimensionality is well defined and has a constant value for most scales of length of the chain renormalisation group theory provides a theoretical basis for the concept of fractal dimensionality in polymers

asymptotically isometric copies of c0 and l1 in bochner spaces abstract let x be a banach space and be a finite measure space it is shown that if 1 p resp 1 p l p x contains asymptotically isometric copies of c 0 resp l 1 if and only if x does

duality on planar fractal and hierarchical lattices duality constructions are presented for the classes of planar fractal and hierarchical lattices interesting results include the interpretation of dual sierpinski gasket and carpets as fractal domain models that the constructions take a lattice l with intrinsic dimension d and connectivity q to a dual l with d d q and q 1 q and a novel but trivial dual for the one dimensional lattice

self avoiding walks on self similar structures finite versus infinite ramification self avoiding walks saws generated by exact enumeration techniques are studied on the sierpinski carpet d 2 and on the sierpinski sponge d 3 also called sierpinski square lattices a detailed comparison of the results for saws on these infinitely ramified fractals to saws on finitely ramified sierpinski gaskets sierpinski triangular lattices on regular lattices and on the incipient percolation cluster is done providing insight into the behaviour of saws on ordered and disordered structures the saws on sierpinski square lattices are found to display a kind of intermediate behaviour sharing aspects of both saws on ordered and on fractal structures as a consequence a des cloizeaux relation does not seem to hold for this structure as opposed to its validity for saws on regular lattices on sierpinski triangular lattices and on the incipient percolation cluster

critical properties of ising models with long range interactions on sierpinski gasket lattices in higher euclidean dimensions abstract ising systems with two spin long range interactions are studied on sierpinski gasket lattices generalized to euclidean dimensions d 3 4 5 6 for each lattice the long range interactions are assigned to edges that are part of the appropriate self similar structure in consequence these systems are infinitely ramified and exhibit critical behavior at finite temperatures an analysis of critical properties of the systems in particular the calculation of critical exponents is carried out by using an exact renormalization group method it is shown that there exists some similarity between critical properties of the long range interacting fractal models under study here and critical properties of short range interacting ising models defined on abstract regular lattices interpolated to noninteger dimensionalities

continuity of dea efficiency measures data envelopment analysis dea is a methodology that allows in one way or other the assignment of efficiency scores to members of a group of decision making units we call an efficiency measure continuous if small perturbations of the input output data cause only small changes in the score continuity is a desirable property of an efficiency measure in particular in the presence of measurement tolerances continuity is also desirable from a numerical point of view because the scores are computed by linear programming software focusing on convex production possibility sets we give examples where radial dea measures fail to be continuous i e they jump under small data perturbations we present necessary and sufficient conditions for continuity in terms of the data and show that these conditions are satisfied for almost all data we also discuss continuity of nonradial measures and identify possible problems of multistage approaches to compute mix efficiencies

critical behavior of the kinetic ising model on a fractal lattice the authors study the critical behaviour static and dynamic of the ising model defined on a fractal sierpinski carpet using monte carlo calculations estimates for various critical exponents are obtained from a finite size scaling analysis the results are compared with the available predictions for the dynamical critical exponent z they find the dynamic exponent z near 2 2 to be lower than predicted

local rotundity structure of generalized orlicz lorentz sequence spaces abstract we give some criteria for extreme points and strong u points in generalized orlicz lorentz sequence spaces which were introduced in p foralewski h hudzik l szymaszkiewicz on some geometric and topological properties of generalized orlicz lorentz sequence spaces math nachr in press cf g g lorentz an inequality for rearrangements amer math monthly 60 1953 176 179 m nawrocki the mackey topology of some f spaces ph d dissertation adam mickiewicz university poznan 1984 in polish some examples show that in these spaces the notion of the strong u point is essentially stronger than the notion of the extreme point this paper is related to the results from a kaminska extreme points in orlicz lorentz spaces arch math 55 1990 173 180 see remark 1

potts model on a fractal lattice the authors consider the dilute potts model on the sierpinski carpet the model has a phase transition at a finite temperature and both critical and tricritical behaviour are observed for qqc where q is the number of potts states they use migdal kadanoff type recursion relations to obtain the value of qc and of critical and tricritical exponents and investigate their dependence on various geometrical characteristics of the fractal

critical behavior of the gaussian model on a diamond type hierarchical lattice with periodic and aperiodic interactions abstract the critical behavior of the gaussian models on a diamond type hierarchical lattice with periodic and aperiodic interactions according to a class of substitution sequences are studied by the exact renormalization group approach and spin rescaling for the periodic case with a two letter general fibonacci sequence given by the generating substitutions a ab b ab and the aperiodic case with the generating substitutions a ab b ba the critical behaviors are found unchanged with respect to the uniform case and belong to the same universality of the uniform case for the other aperiodic case with the generating substitutions a ab b aa the geometric fluctuation is relevant by luck s criterion and the critical phenomena of the uniform and periodic cases are found to disappear

multiplicative aggregation of division efficiencies in network data envelopment analysis abstract network systems have two basic structures series and parallel and a network system can be transformed into a series system of subsystems where each has a parallel structure composed of a number of divisions the efficiency of the system can thus be expressed as the product of those of the subsystems and the efficiency of each subsystem is a weighted average of those of its component divisions under a relational data envelopment analysis dea model a previous study showed that the efficiency of a network system can be expressed as an additive aggregation of those of the divisions adjusted by a factor and the former is bounded from above by the latter this paper shows that the efficiency of the system can be expressed as a multiplicative aggregation of those of the divisions multiplied by a factor of greater than one the system efficiency is thus bounded from below by the multiplicative aggregation of the division efficiencies an example is used to show how to calculate the efficiency bounds and how to identify the divisions that have stronger effects on the performance of the system

noninteger dimensional hyper euclidean lattices on sierpinski carpets random walks on sierpinski carpets are studied with bond moving renormalisation using the results the author constructs fractal lattices whose fractal dimension of random walk is two such fractal lattices are called hyper euclidean lattices it turns out that hyper euclidean lattices have a connectivity which is one smaller than the fractal dimension

deterministic models of fractal and multifractal growth abstract four deterministic models are presented in order to get more insight into the geometry and multifractal behavior associated with fractal growth phenomena these models allow for exact treatment and are used to demonstrate such properties as directed self affinity and self similarity and multifractal growth probability and mass distribution it is pointed out that in some cases the various fractal dimension definitions may lead to inconsistent results

new method of analysing self avoiding walks in four dimensions a new method based on the concept of fractal dimensionality is used to study the problem of self avoiding walks in a four dimensional lattice the authors find from monte carlo simulations that the confluent logarithmic exponent related to the end to end distance is 1 8 or 0 01 in excellent agreement with the prediction derived from the n to 0 vector model

dual fixed point property on spaces of continuous functions under equivalent norms abstract a banach space x is said to have the fixed point property if for every closed convex bounded subset c x and for every t c c nonexpansive there is a fixed point a banach space is said to have the dual fixed point property if its dual space x verifies the fixed point property it is a fact that c 0 k fails the dual fixed point property for every locally compact hausdorff set k in this article we study the fulfilment of the dual fixed point property under equivalent norms we prove that c 0 k can be renormed to have the dual fixed point property if and only if k is a countable set in this case we prove that this renorming can be achieved as close to the standard norm on c 0 k as we like for the banach mazur distance we further obtain the corresponding weak fixed point property stability coefficient regarding the duality c 0 k c 0 k it will be displayed that the value of this stability coefficient strongly depends on the distribution of the accumulation points of k finally we prove that the dual fixed point property is completely unstable for the banach mazur distance in most of nonreflexive banach spaces

an assurance interval for the non archimedean epsilon in dea models this paper clarifies the role of non archimedean infinitesimal e in dea models so that the associated linear programs may be infeasible for the multiplier side and unbounded for the envelopment side for certain values of e it is shown that the bound of e proposed by ali and seiford 1993 is invalid for feasibility and boundedness of the linear programs a procedure is presented for determining an assurance interval of e it is also shown that an assurance value for e can be found using a single linear program

quantum field theory models on fractal spacetime i introduction and overview deux types de modeles de champs scalaires sont consideres l un a son propagateur donne par un temps propre ou une representation chaleur noyau l autre a un propagateur hierarchique la version du reseau fractal du propagateur a temps propre est une reflexion positive

a suggested lacunarity expression for sierpinski carpets a suggested approximate expression for lacunarity is proposed some numerical investigations show that the old expression fails in describing the homogeneity of elimination for some sierpinski carpets

exact renormalization group treatment of the piecewise directed random walks on fractals abstract an exact evaluation of the critical exponent v associated with the mean squared end to end distance of the piecewise directed random walks is presented in the case of the complete family of the sierpinski gasket type of fractals

self referred approach to lacunarity this paper describes an approach to lacunarity which adopts the pattern under analysis as the reference for the sliding window procedure the superiority of such a scheme with respect to more traditional methodologies especially when dealing with finite size objects is established and illustrated through applications to diffusion limited aggregation pattern characterization it is also shown that given the enhanced accuracy and sensitivity of this scheme the shape of the window becomes an important parameter with advantage for circular windows

lacunarity and universality a new expression for the lacunarity of sierpinski carpets is proposed it turns out that the universality can be described with the new expression the fractal dimension and the connectivity

scale dependent lacunarity and fractal ising models as an alternate way of measuring the lacunarity of sierpinski carpets the authors have computed the site to site fluctuation of the quantity m n namely the total number of lattice sites within the chemical distance of n in long scales of n the resultant lacunarity agrees qualitatively with the results obtained in the past using the covering method in short scales of n however the lacunarity shows a different trend among fractals it varies monotonically with the ising correlation length exponent a trend which was sought before but not found with the previous method this applies only for the carpets of the first kind

asymptotically isometric copies of c0 and l1 in certain banach spaces abstract if x is a separable banach space then x contains an asymptotically isometric copy of l1 if and only if there exists a quotient space of x which is asymptotically isometric to c0 if x is an infinite dimensional normed linear space and y is any banach space containing an asymptotically isometric copy of c0 then l x y contains an isometric copy of l if x and y are two infinite dimensional banach spaces and y contains an asymptotically isometric copy of c0 then k w x y contains a complemented asymptotically isometric copy of c0

exact results for an ising system with long range interactions on the sierpinski gasket lattice thermodynamic properties of an ising model with two point long range interactions on the sierpinski gasket lattice are studied using an exact recursive methodfor calculating the partition function the long range interactions are introduced in a self similar manner reflecting the structure of the lattice and are assumed to be of the form ql q 2 l 1 where q 0 0 are parameters and l 1 2 indicates that ql couples pairs of spins on the distance 2l measured in units of the lattice spacing in the case of constant long range interactions 0 exact analytic expression for the critical temperature and the critical exponent v are derived it is also shown that the recursive method can be applied to analyze the problem of the existence of phase transitions at finite temperatures in the case of 0 i e when the long range coupling decrease with the distance

bounds for the fractal dimension of space the authors discuss the possibility that space has to be described as being of non integer dimension they elaborate on some of the problems associated with this idea and investigate the chance to observe effects due to such a fractional dimension two experiments show rather stringent bounds for the deviation of the space dimension from the value three these are the perihelion shift of planetary motion and the lamb shift in hydrogen

self similar and translationally invariant structures in a bond diluted ising model a bond diluted ising model is used to simulate a process from a cantor set to a translationally invariant lattice the free energy function shows that there is no singularity which seem to imply that no transition exists in this process

on the fractal distribution of primes and prime indexed primes by the binary image analysis abstract in this paper the distribution of primes and prime indexed primes pips is studied by mapping primes into a binary image which visualizes the distribution of primes these images show that the distribution of primes and pips is similar to a cantor dust moreover the self similarity with respect to the order of pips already proven in batchko 2014 can be seen as an invariance of the binary images the index of primes plays the same role of the scale for fractals so that with respect to the index the distribution of prime indexed primes is characterized by the self similarity alike any other fractal in particular in order to single out the scale dependence the pips fractal distribution will be evaluated by limiting to two parameters fractal dimension and lacunarity that are usually used to measure the fractal nature because of the invariance of the corresponding binary plots the fractal dimension and lacunarity of primes distribution are invariant with respect to the index of pips

critical behaviour of the long range interaction model on a fractal lattice a particular class of fractal lattices is considered where the ising model with power law decaying interactions can be well approximated to a hierarchical type model applying the exact recurrence relations the critical behaviour is calculated and its universality with respect to the fractal dimensionality d is examined

remarks on duality lattices and the sierpinski gasket duality constructions for the sierpinski gasket and other fractals are studied coxeter s definition 1969 of a dual lattice is used to prove the existence of two kinds of dual lattice for the sierpinski gasket

the daugavet property in the musielak orlicz spaces abstract we show that among all musielak orlicz function spaces on a finite non atomic complete measure space equipped with either the luxemburg norm or the orlicz norm the only spaces with the daugavet property are l 1 l l 1 1 l and l 1 l in particular we obtain complete characterizations of the daugavet property in the weighted interpolation spaces the variable exponent lebesgue spaces nakano spaces and the orlicz spaces

classification and universal properties of sierpinski carpets the type of critical points for the potts model is found to be dependent on the structure of sierpinski carpets all possible types of structure for sierpinski carpets with two interactions after bond moving are found the author presents general sierpinski carpets and new parameters are proposed and used to describe them the lacunarity expression is revised the author discusses and proposes a universal classification critical points eigenvalues and flow diagrams are presented some fixed points display negative eigenvalues

potts model on sierpinski carpets migdal kadanoff bond moving renormalisation is used to study the q state potts model on sierpinski carpets a general approximate recursion relation including q as a parameter is given the property of bond interchanging invariance is found and used in deriving the recursion relation fixed points and critical exponents for some carpets are presented marginal fixed points instead of unstable ones are found several typical flow diagrams are also shown

renormings failing to have asymptotically isometric copies of l1 or c0 abstract it is proved that every equivalent norm in l 1 is the starting point of a ray of norms which fail to have an asymptotically isometric copy of l 1 in the case where x is separable it is proved that the set of all equivalent norms in x which fail to have an asymptotically isometric copy of l 1 is residual similar results are obtained for the case of c 0 in particular we deduce that every separable banach space has an equivalent norm for which it fails to contain an asymptotically isometric copy of l 1 and c 0

asymptotically isometric copies ofc0and renormings of banach spaces abstract if a banach space x contains an asymptotically isometric copy of c 0 then x fails to have weak normal structure consequently if x is an infinite dimensional subspace of c 0 then x fails to have weak normal structure also every equivalent renorming of c 0 for uncountable fails to have weak normal structure every separable banach space can be equivalently renormed so as not to contain an asymptotically isometric copy of c 0 every banach space with the generalized gossez lami dozo ggld property fails to contain a subspace isomorphic to c 0

percolation on infinitely ramified fractals we present a family of exact fractals with a wide range of fractal and fracton dimensionalities this includes the case of the fracton dimensionality of 2 which is critical for diffusion this is achieved by adjusting the scaling factor as well as an internal geometrical parameter of the fractal these fractals include the cases of finite and infinite ramification characterized by a ramification exponentp the infinite ramification makes the problem of percolation on these lattices a nontrivial one we give numerical evidence for a percolation transition on these fractals this transition is tudied by a real space renormalization group technique on lattices with fractal dimensionality d between 1 and 2 the critical exponents for percolation depend strongly on the geometry of the fractals

critical behaviour of the bond diluted potts model on sierpinski carpets a four parameter bond moving renormalisation is used to study the critical properties of the bond diluted q state potts model on sierpinski carpets fixed points critical exponents and a phase diagram are obtained in the authors results there is a borderline value q qt for q qt there is crossover to a new diluted fixed point this behaviour is similar to that of the diluted system on a regular lattice with translational invariance they give some values of qt for carpets with different b l where b and l are structure parameters of carpets

phase transitions on fractals i quasi linear lattices magnetic spin models and resistor networks are studied on certain self similar fractal lattices which are described as quasi linear because they share a significant property of the line finite portions can be isolated from the rest by removal of two points sites in all cases there is no long range order at finite temperature the transition at zero temperature has a discontinuity in the magnetisation and the associated magnetic exponent is equal to the fractal dimensionality d when the lattice reduces to a non branching curve the thermal exponent v 1 y is equal to d when the lattice is a branching curve y is related respectively to the dimensionality of the single channel segments of the curve for the ising model or to the exponent describing the resistivity for models with continuous spin symmetry

banach spaces with the daugavet property a banach space x is said to have the daugavet property if every operator t x x of rank 1 satisfies 11 id tl 1 fltil we show that then every weakly compact operator satisfies this equation as well and that x contains a copy of t1 however x need not contain a copy of l1 we also study pairs of spaces x c y and operators t x y satisfying i i j t i i 1 4 1f t i i where j x y is the natural embedding this leads to the result that a banach space with the daugavet property does not embed into a space with an unconditional basis in another direction we investigate spaces where the set of operators with f id tll 1 il t l i is as small as possible and give characterisations in terms of a smoothness condition