percolation transitions in two dimensions we investigate bond and site percolation models on several two dimensional lattices numerically by means of transfer matrix calculations and monte carlo simulations the lattices include the square triangular honeycomb kagome and diced lattices with nearest neighbor bonds and the square lattice with nearest and next nearest neighbor bonds results are presented for the bond percolation thresholds of the kagome and diced lattices and the site percolation thresholds of the square honeycomb and diced lattices we also include the bond and site percolation thresholds for the square lattice with nearest and next nearest neighbor bonds we find that corrections to scaling behave according to the second temperature dimension xt2 4 predicted by the coulomb gas theory and the theory of conformal invariance in several cases there is evidence for an additional term with the same exponent but modified by a logarithmic factor only for the site percolation problem on the triangular lattice does such a logarithmic term appear to be small or absent the amplitude of the power law correction associated with xt2 4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems

on generalized methods of successive approximations abstract there are several generalized methods of monotone successive approximations in ordered sets a which generalize the usual sequences of the iterative of a point a of a under a selfmapping f on a to some well ordered subsets of a these are smallest admissible set containing a by buber and kirk the set w a by abian and brown well ordered chain of f iterations of a by heikkila and smallest complete f chain containing a by fuchssteiner the well ordered chains of f iterations were compared by heikkila in 1999 with the admissible sets we compare here all of the above four methods our study is based on a notion of a generalized orbit which is a generalization of the one which was introduced by the author in 1988 as an answer to a problem posed by banaschewski in 1992 we use in our proofs a minimum of tools in particular we assume that the relation is only asymmetric we do not use the transitivity postulated for orderings and use only extensionality pairing union and separation axioms of zermelo s set theory

anomaly of the height height correlation functions in self flattening surface growth by monte carlo simulations and scaling theories we consider the height height correlation function g r t l of the one dimensional equilibrium self flattening surface growths where the deposition evaporation attempt only at the globally highest lowest site is suppressed g r t l is shown to satisfy the anomalous scaling behavior g r t l l 2alpha g 1 r l delta t l z or g r t l t 2beta g 2 r t 1 z l t 1 z here alpha beta and z are the roughness growth and dynamic exponents respectively for the surface width with alpha 1 3 and z alpha beta 3 2 anomalous exponents z and delta are found to satisfy z 9 4 and delta z z we also show that anomalous behavior of g r t l can be understood from a scaling theory based on the competition between local random walk like behavior and the global length scale suppression

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

equilibrium restricted solid on solid growth model on fractal substrates the equilibrium restricted solid on solid growth model on fractal substrates is studied by introducing a fractional langevin equation the growth exponent beta and the roughness exponent alpha defined respectively by the surface width via w approximately t beta and the saturated width via w sat approximately l alpha l being the system size were obtained by a power counting analysis and the scaling relation 2alpha d f z rw was found to hold the numerical simulation data on sierpinski gasket checkerboard fractal and critical percolation cluster were found to agree well with the analytical predictions of the fractional langevin equation

surface growth and crossover behaviour in a restricted solid on solid model the authors describe results of numerical simulations of growth in a restricted solid on solid model they first extract the exponent beta by comparing the surface width w t approximately tbeta with a spatially averaged height correlation function g t the latter is shown to give a more accurate estimate for beta even for relatively small systems the exponent x is obtained from the saturation of the interface fluctuations in the late time regime their results lead to a conjecture of dimension dependent exponents as beta d 1 d 1 x d 2 d 2 in addition they study time dependent crossover phenomena by relaxing the local height constraint and using a noise reduction method in the model they demonstrate how the effect of such crossover effects may lead to spurious values of the growth exponents finally they discuss their results in relation to other discrete models and the continuum growth equations

symmetric orthogonal filters and wavelets with linear phase moments in this paper we study symmetric orthogonal filters with linear phase moments which are of interest in wavelet analysis and its applications we investigate relations and connections among the linear phase moments sum rules and symmetry of an orthogonal filter as one of the results we show that if a real valued orthogonal filter a is symmetric about a point then a has sum rules of order m if and only if it has linear phase moments of order 2m these connections among the linear phase moments sum rules and symmetry help us to reduce the computational complexity of constructing symmetric real valued orthogonal filters and to understand better symmetric complex valued orthogonal filters with linear phase moments to illustrate the results in the paper we provide many examples of univariate symmetric orthogonal filters with linear phase moments in particular we obtain an example of symmetric real valued 4 orthogonal filters whose associated orthogonal 4 refinable function lies in c 2 r

multivariate refinable functions differences and ideals a simple tutorial this paper summarizes the algebraic quotient ideal approach to polynomial generation by refinable functions and connects it to strang fix conditions and factorization with respect to difference operators motivated by the latter one we also consider vector subdivision schemes with matrix valued coefficients and review some of their properties

on extremal solutions of inclusion problems with applications to game theory abstract a recursion principle generalized iteration methods and the axiom of choice are applied to prove the existence of extremal fixed points of set valued mappings in posets extremal solutions of an inclusion problem and extremal nash equilibria for a normal form game

surface growth on percolation networks by a conserved noise restricted solid on solid growth model surface growth by the conserved noise restricted solid on solid model is investigated on diluted lattices i e on percolation networks that are embedded in two spatial dimensions the growth exponent and the roughness exponent are defined respectively by the mean square surface width via w 2 t t 2 and the mean square saturated width via w sat 2 l l 2 where l is the system size these are measured on both an infinite network and a backbone network and the results are compared with power counting predictions obtained using the fractional langevin equation while the monte carlo results on deterministic fractal substrates show excellent agreement with the predictions d h kim and j m kim phys rev e 84 011105 2011 the results on critical percolation networks deviate by 8 12 from these predictions

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

numerical study of the kardar parisi zhang equation we integrate numerically the kardar parisi zhang kpz equation in 1 1 and 2 1 dimensions using a euler discretization scheme and the replacement of nablah 2 by exponentially decreasing functions of that quantity to suppress instabilities when applied to the equation in 1 1 dimensions the method of instability control provides values of scaling amplitudes consistent with exactly known results in contrast to the deviations generated by the original scheme in 2 1 dimensions we spanned a range of the model parameters where transients with edwards wilkinson or random growth are not observed in box sizes 8 or l or 128 we obtain a roughness exponent of 0 37 or alpha or 0 40 and steady state height distributions with skewness s 0 25 0 01 and kurtosis q 0 15 0 1 these estimates are obtained after extrapolations to the large l limit which is necessary due to significant finite size effects in the estimates of effective exponents and height distributions on the other hand the steady state roughness distributions show weak scaling corrections and evidence of stretched exponential tails these results confirm previous estimates from lattice models showing their reliability as representatives of the kpz class

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

surface growth on diluted lattices by a restricted solid on solid model an influence of diluted sites on surface growth has been investigated using the restricted solid on solid model it was found that with respect to equilibrium growth the surface width and the saturated width exhibited universal power law behaviors i e w ensuremath sim t ensuremath beta and w text sat ensuremath sim l ensuremath zeta regarding all cases with respect to the concentration of diluted sites x 1 ensuremath p with p being the occupation probability on each lattice site for xl x c 1 ensuremath p c p c being the percolation threshold the growth appeared to be similar to that of a regular lattice both in two and three dimensions for x x c the growth yielded nontrivial exponents which were different from those on a regular lattice in nonequilibrium growth a considerable amount of diluted sites x ensuremath le x c appeared to yield nonuniversal growth unlike the case of a regular lattice the cause of nonuniversal growth dynamics has been investigated considering the growth on a backbone cluster and on lattices constructed with periodically and randomly diluted subcells

width distributions and the upper critical dimension of kardar parisi zhang interfaces simulations of restricted solid on solid growth models are used to build the width distributions of d 2 5 dimensional kardar parisi zhang kpz interfaces we find that the universal scaling function associated with the steady state width distribution changes smoothly as d is increased thus strongly suggesting that d 4 is not an upper critical dimension for the kpz equation the dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity

the structure of balanced multivariate biorthogonal multiwavelets and dual multiframelets multiwavelets and multiframelets are of interest in several applications such as numerical algorithms and signal processing due to their desirable properties such as high smoothness and vanishing moments with relatively small supports of their generating functions and masks in order to process and represent vector valued discrete data efficiently and sparsely by a multiwavelet transform a multiwavelet has to be prefiltered or balanced balanced orthonormal univariate multiwavelets and multivariate biorthogonal multiwavelets have been studied and constructed in the literature dual multiframelets include bi orthogonal multiwavelets as special cases but their fundamental prefiltering and balancing property has not yet been investigated in the literature in this paper we shall study the balancing property of multivariate multiframelets from the point of view of the discrete multiframelet transform this approach to our best knowledge has not been considered so far in the literature even for multiwavelets but it reveals the essential structure of prefiltering and the balancing property of multiwavelets and multiframelets we prove that every biorthogonal multiwavelet can be prefiltered with the balancing order matching the order of its vanishing moments that is from every given compactly supported multivariate biorthogonal multiwavelet one can always build another essentially equivalent compactly supported biorthogonal multiwavelets with its balancing order matching the order of the vanishing moments of the original one more generally we show that if a dual multiframelet can be prefiltered then it can be equivalently transformed into a balanced dual multiframelet with the same balancing order however we notice that most available dual multiframelets in the literature cannot be simply prefiltered with its balancing order matching its order of vanishing moments and they must be designed to possess high balancing orders the key ingredient of our approach is based on investigating some properties of the subdivision and transition operators acting on discrete vector polynomial sequences which play a central role in a discrete multiframelet transform and are of interest in their own right we also establish a new canonical form of a matrix mask which greatly facilitates the investigation and construction of multiwavelets and multiframelets in this paper we obtain a complete criterion and the essential structure for balanced or prefiltered dual multiframelets in the most general setting our investigation of the balancing property of a multiframelet deepens our understanding of the multiframelet transform in signal processing and scientific computation

existence and comparison results for operator and differential equations in abstract spaces in this paper we apply the chain methods developed in heikkila and lakshmikantham 1994 to obtain new fixed point theorems and new existence and comparison results for operator equations in partially ordered sets these results are then applied to discontinuous implicit functional differential equations in ordered banach spaces

existence results for operator and differential equations and inclusions abstract this paper contains a brief summary of existence results for operator and differential equations and inclusions derived recently via a recursion method and generalized iteration methods introduced in 11 12 23

height height correlations for surface growth on percolation networks abstract the height height correlations of the surface growth for equilibrium and nonequilibrium restricted solid on solid rsos model were investigated on randomly diluted lattices i e on infinite percolation networks it was found that the correlation function calculated over the chemical distances reflected the dynamics better than that calculated over the geometrical distances for the equilibrium growth on a critical percolation network the correlation function for the evolution time t 1 yielded a power law behavior with the power associated with the roughness exponent via the relation d f d l with d f and d l being respectively the fractal dimension and the chemical dimension of the substrate for the nonequilibrium growth on the other hand the correlation functions did not yield power law behaviors for the concentration of diluted sites x less than or equal to the critical concentration x c

critical dynamics of the contact process with quenched disorder we study critical spreading in monte carlo simulations of the two dimensional contact process cp with quenched disorder in the form of random dilution in the pure model spreading from a single particle at the critical point ensuremath lambda c follows power laws with the critical exponents of directed percolation with disorder critical spreading is logarithmic not power law below ensuremath lambda c there is a griffiths phase in which the time dependence is governed by nonuniversal power laws the effects of disorder are also apparent above ensuremath lambda c in the active phase where the relaxation of the survival probability is algebraic rather than exponential as in the pure model our results support the conjecture by bramson durrett and schonmann ann prob 19 960 1991 that in two or more dimensions the disordered cp has only a single phase transition

an algorithm for matrix extension and wavelet construction this paper gives a practical method of extending an n x r matrix p z r n with laurent polynomial entries in one complex variable z to a square matrix also with laurent polynomial entries if p z has orthonormal columns when z is restricted to the torus t it can be extended to a paraunitary matrix if p z has rank r for each z t it can be extended to a matrix with nonvanishing determinant on t the method is easily implemented in the computer it is applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

approximation properties of multivariate wavelets wavelets are generated from refinable functions by using multiresolution analysis in this paper we investigate the approximation properties of multivariate refinable functions we give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask we connect the approximation properties of a refinable function with the spectral properties of the corresponding subdivision and transition operators finally we demonstrate that a refinable function in w k 1 1 r s provides approximation order k