coupled fixed point theorems for multi valued nonlinear contraction mappings in partially ordered metric spaces abstract in this paper we establish two coupled fixed point theorems for multi valued nonlinear contraction mappings in partially ordered metric spaces the theorems presented extend some results due to ciric 2009 3 an example is given to illustrate the usability of our results

fixed points and approximate solutions for nonlinear operator equations we study a nonlinear operator equation and obtain a sequence of approximate solutions by extending the monotone iterative technique to new situations some examples and applications are presented

coincidence and common fixed point theorems for a sequence of mappings in ordered metric spaces in this article the existence of coincidence points and common fixed points for a sequence of mappings satisfying generalized weakly contractive conditions which involves altering distance functions without exploiting the notion of continuity of any map involved therein in a ordered metric space is proved an example is given to support the usability of our results

characterizations of reproducing cones and uniqueness of fixed points the purpose of this paper is to discuss the existence and uniqueness of fixed point in a partially ordered banach space based on the characterizations of reproducing cones some fixed point theorems for nonlinear operators are proved as an application the existence and uniqueness of periodical solution for a first order differential equation is discussed

kardar parisi zhang universality class and the anchored toom interface we revisit the anchored toom interface and use kardar parisi zhang scaling theory to argue that the interface fluctuations are governed by the airy1 process with the role of space and time interchanged the predictions which contain no free parameter are numerically well confirmed for space time statistics in the stationary state in particular the spatial fluctuations of the interface computed numerically agree well with those given by the goe edge distribution of tracy and widom

coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces abstract we introduce the concept of a mixed g monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces presented theorems are generalizations of the recent fixed point theorems due to bhaskar and lakshmikantham t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 and include several recent developments

exact solution for the stationary kardar parisi zhang equation we obtain the first exact solution for the stationary one dimensional kardar parisi zhang equation a formula for the distribution of the height is given in terms of a fredholm determinant which is valid for any finite time t the expression is explicit and compact enough so that it can be evaluated numerically furthermore by extending the same scheme we find an exact formula for the stationary two point correlation function

kardar parisi zhang equation in the weak noise limit pattern formation and upper critical dimension we extend the previously developed nonperturbative weak noise scheme applied to the noisy burgers equation in one dimension to the kardar parisi zhang equation for a growing interface in arbitrary dimensions by means of the cole hopf transformation we show that the growth morphology can be interpreted in terms of dynamically evolving textures of localized growth modes with superimposed diffusive modes in the cole hopf representation the growth modes are static solutions to the diffusion equation and the nonlinear schrodinger equation subsequently boosted to finite velocity by a galilei transformation we discuss the dynamics of the pattern formation and briefly the superimposed linear modes implementing the stochastic interpretation we discuss kinetic transitions and in particular the preliminary scaling properties pertaining to the pair mode or dipole sector in the dipole sector we obtain the hurst exponent h 3 d 4 d or dynamic exponent zdip 4 d 3 d for the random walk of growth modes below d 3 the dipole growth modes show anomalous diffusion above d 3 the dipole growth modes freeze finally applying derrick s theorem based on constrained minimization we show that the upper critical dimension is d 4 in the sense that growth modes cease to exist above this dimension

new fixed point theorems and applications of mixed monotone operator in this paper we study the uniqueness and existence of fixed point of mixed monotone operators in the partially ordered banach space the results extend and improve recent related results

width distribution for random walk interfaces roughening of a one dimensional interface is studied under the assumption that the interface configurations are continuous periodic random walks the distribution of the square of the width of interface mathit w 2 is found to scale as p mathit w 2 mathit w 2 mathrm mathrm ensuremath 1 ensuremath phi mathit w 2 mathit w 2 where mathit w 2 is the average of mathit w 2 we calculate the scaling function ensuremath phi x exactly and compare it both to exact enumerations for a discrete slope surface evolution model and to ensuremath phi s obtained in monte carlo simulations of equilibrium and driven interfaces of chemically reacting systems

on the coefficient quantization of the fourier basis a family of function bases is devised from a superposition of unit characteristic functions it is shown that these simple bases can be used to perform a quantized fourier transform furthermore the transform can be implemented in an iterative scheme such that system resources are balanced in accordance with performance

coincidence and fixed point theorems for generalized ψ φ weak nonlinear contraction in ordered k metric spaces in this paper we establish coincidence and fixed point theorems for a pair of mappings satisfying a new generalized j f weak nonlinear contraction type condition in ordered k metric spaces the presented results generalize and extend the very recent results of choudhury and metiya b s choudhury and n metiya the point of coincidence and common fixed point for a pair of mappings in cone metric spaces computers and mathematics with applications 60 2010 1686 1695

new square wave transform for digital signal processing a novel transform for spectral decomposition that uses regular square waves as the basis functions is presented the digital transform requires order n operations the transform possesses unusually symmetry properties which may prove useful in many applications in particular it can act as a generalized frequency filter that only depends on the periodicity of the data

nonperturbative renormalization group for the stationary kardar parisi zhang equation scaling functions and amplitude ratios in 1 1 2 1 and 3 1 dimensions we investigate the strong coupling regime of the stationary kardar parisi zhang equation for interfaces growing on a substrate of dimension d 1 2 and 3 using a nonperturbative renormalization group nprg approach we compute critical exponents correlation and response functions extract the related scaling functions and calculate universal amplitude ratios we work with a simplified implementation of the second order in the response field approximation proposed in a previous work phys rev e 84 061150 2011 and phys rev e 86 019904 e 2012 which greatly simplifies the frequency sector of the nprg flow equations while keeping a nontrivial frequency dependence for the two point functions the one dimensional scaling function obtained within this approach compares very accurately with the scaling function obtained from the full second order nprg equations and with the exact scaling function furthermore the approach is easily applicable to higher dimensions and we provide scaling functions and amplitude ratios in d 2 and d 3 we argue that our ansatz is reliable up to d symbol see text 3 5

critical exponents of the kpz equation via multi surface coding numerical simulations we study the kpz equation in d 2 3 and 4 spatial dimensions by using a restricted solid on solid discretization of the surface we measure the critical exponents very precisely and we show that the rational guess is not appropriate and that d 4 is not the upper critical dimension we are also able to determine very precisely the exponent of the sub leading scaling corrections that turns out to be close to unity in all cases we introduce and use a multi surface coding technique that allows a gain of the order of 30 fold over usual numerical simulations

fixed point theorems for weakly c contractive mappings in ordered metric spaces the purpose of this paper is to present some fixed point results for weakly c contractive mappings in a complete metric space endowed with a partial order

universality of fluctuations in the kardar parisi zhang class in high dimensions and its upper critical dimension we show that the theoretical machinery developed for the kardar parisi zhang kpz class in low dimensions is obeyed by the restricted solid on solid model for substrates with dimensions up to d 6 analyzing different restriction conditions we show that the height distributions of the interface are universal for all investigated dimensions it means that fluctuations are not negligible and consequently the system is still below the upper critical dimension at d 6 the extrapolation of the data to dimensions d 7 predicts that the upper critical dimension of the kpz class is infinite

common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces in the first part of this paper we generalize results on common fixed points in ordered cone metric spaces obtained by i altun and g durmaz i altun g durmaz some fixed point theorems on ordered cone metric spaces rend circ mat palermo 58 2009 319 325 and i altun b damnjanovic and d djoric i altun b damnjanovic d djoric fixed point and common fixed point theorems on ordered cone metric spaces appl math lett 2009 doi 10 1016 j aml 2009 09 016 by weakening the respective contractive condition then the notions of quasicontraction and g quasicontraction are introduced in the setting of ordered cone metric spaces and respective common fixed point theorems are proved in such a way known results on quasicontractions and g quasicontractions in metric spaces and cone metric spaces are extended to the setting of ordered cone metric spaces examples show that there are cases when new results can be applied while old ones cannot

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

generalized weak contractions in partially ordered metric spaces recent results of doric d doric common fixed point for generalized j f weak contractions appl math lett 22 2009 1896 1900 on generalized weakly contractive mappings are extended to the setting of partially ordered metric spaces thus generalization of fixed point results of harjani and sadarangani j harjani k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear anal 71 2009 3403 3410 is obtained some applications are presented examples are given to show that our results are proper generalizations of the existing ones

polymers on disordered hierarchical lattices a nonlinear combination of random variables the problem of directed polymers on disordered hierarchical and hypercubic lattices is considered for the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way we present the results of numerical simulations of two hierarchical lattices finding evidence of a phase transition in one case for a limiting case we extend the perturbation theory developed by derrida and griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties overlaps of the model in this limit we obtain an interpolation formula allowing one to obtain the noninteger moments of the partition function from the integer moments we obtain bounds for the transition temperature for hierarchical and hypercubic lattices and some similarities between the problem on the two different types of lattice are discussed

upper critical dimension of the kardar parisi zhang equation numerical results for the directed polymer model in 1 4 dimensions in various types of disorder are presented the results are obtained for a system size that is considerably larger than considered previously for the extreme strong disorder case min max system associated with the directed percolation model the expected value of the meandering exponent 0 5 is clearly revealed with very weak finite size effects for the weak disorder case associated with the kardar parisi zhang equation finite size effects are stronger but the value of is clearly seen in the vicinity of 0 57 in systems with strong disorder it is expected that the system will cross over sharply from min max behavior at short chains to weak disorder behavior at long chains our numerical results agree with that expectation to complete the picture we obtain the energy fluctuation exponent for weak disorder and we find that the value of is in the vicinity of 0 14 thus the meandering exponent and the energy fluctuation exponent obey the strong coupling scaling relation 2 1 our results indicate that 1 4 is not the upper critical dimension in the weak disorder case and thus 4 1 does not seem to be the upper critical dimension for the kardar parisi zhang equation

vectorized and parallel simulations of the kardar parisi zhang equation in 3 1 dimensions the kardar parisi zhang kpz equation describing kinetic roughening is solved numerically for 3 1 dimensional systems in the strong coupling phase by massive use of supercomputing tools we calculate for the first time the exponent beta 0 181 or 0 007 with an accuracy comparable with that of lattice growth model simulations a possible source of errors in parallel monte carlo calculations is pointed out

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

fixed point theorems for generalized contractions in ordered metric spaces abstract the purpose of this paper is to present some fixed point results for self generalized contractions in ordered metric spaces our results generalize and extend some recent results of a c m ran m c reurings a c m ran m c reurings a fixed point theorem in partially ordered sets and some applications to matrix equations proc amer math soc 132 2004 1435 1443 j j nieto r rodriguez lopez j j nieto r rodriguez lopez contractive mapping theorems in partially ordered sets and applications to ordinary differential equations order 22 2005 223 239 j j nieto r rodriguez lopez existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations acta math sin engl ser 23 2007 2205 2212 j j nieto r l pouso r rodriguez lopez j j nieto r l pouso r rodriguez lopez fixed point theorem theorems in ordered abstract sets proc amer math soc 135 2007 2505 2517 a petrusel i a rus a petrusel i a rus fixed point theorems in ordered l spaces proc amer math soc 134 2006 411 418 and r p agarwal m a el gebeily d o regan r p agarwal m a el gebeily d o regan generalized contractions in partially ordered metric spaces appl anal in press as applications existence and uniqueness results for fredholm and volterra type integral equations are given

existence and uniqueness of common fixed points for two multivalued operators in ordered metric spaces in this paper we discuss some new fixed point theorems for a pair of multivalued operators which satisfy weakly generalized contractive conditions our results are the extension and improvement of corresponding results of j harjani and k sadarangani fixed point theorems for weakly contractive mappings in partially ordered sets nonlinear analysis 71 2009 3403 3410 and x zhang common fixed point theorems for some new generalized contractive type mappings j math anal appl 333 2007 780 786 finally some examples are given to illustrate the usability of our results

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

universal aspects of curved flat and stationary state kardar parisi zhang statistics motivated by the recent exact solution of the stationary state kardar parisi zhang kpz statistics by imamura and sasamoto phys rev lett 108 190603 2012 as well as a precursor experimental signature unearthed by takeuchi phys rev lett 110 210604 2013 we establish here the universality of these phenomena examining scaling behaviors of directed polymers in a random medium the stochastic heat equation with multiplicative noise and kinetically roughened kpz growth models we emphasize the value of cross kpz class universalities revealing crossover effects of experimental relevance finally we illustrate the great utility of kpz scaling theory by an optimized numerical analysis of the ulam problem of random permutations

coincidence point theorem for generalized weakly contractions in ordered metric spaces abstract in this article we establish two coincidence point theorems for four mappings satisfying a generalized weakly contractive condition in ordered metric space and apply it to find new coincidence point and common fixed point results we furnish suitable examples to demonstrate the validity of the hypotheses of our results also we give an existence theorem for common solution of two integral equations

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

the point of coincidence and common fixed point for a pair of mappings in cone metric spaces in this paper the existence of a point of coincidence and a common fixed point for two weakly compatible maps on a cone metric space has been established the two mappings are assumed to satisfy certain weak inequalities supporting examples are also given

fixed point results for mappings satisfying ψ φ weakly contractive condition in partially ordered metric spaces abstract we establish coincidence fixed point and common fixed point theorems for mappings satisfying weakly contractive condition in an ordered complete metric space some applications of our obtained results are given

directed polymers in a random medium abstract the problem of a polymer in a random medium can be formulated as follows consider a regular lattice with on each bond ij a random energy ij the energy e w of a self avoiding walk w on this lattice is the sum of the energies of all the bonds visited by the walk then the problem is to compute the partition function z w exp e w t several recent results will be presented 1 the mean field version of this problem can be solved exactly and one observes a low temperature phase similar to the spin glass phase 2 for finite dimensional lattices one can derive bounds on the transition temperature in high enough dimension 3 for hierarchical lattices the problem can be reduced to finding stable laws when one combines random variables in a non linear way for example z z 1 z 2 z 3 z 4

fixed point theorems for mixed monotone operators and applications to integral equations abstract the purpose of this paper is to present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions we also present an application to integral equations

fixed point theorems for weakly contractive mappings in partially ordered sets abstract the purpose of this paper is to present some fixed point theorems for weakly contractive maps in a complete metric space endowed with a partial order

probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension d 1 2 3 via a monte carlo procedure in the disorder in order to probe with high precision the tails of the ground state energy distribution of disordered spin systems k orner katzgraber and hartmann have recently proposed an importance sampling monte carlo markov chain in the disorder in this paper we combine their monte carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground state energy distribution p d e 0 for the directed polymer in a random medium of dimension d 1 2 3 in d 1 we check the validity of the algorithm by a direct comparison with the exact result namely the tracy widom distribution in dimensions d 2 and d 3 we measure the negative tail up to ten standard deviations which correspond to probabilities of order p d e 0 ensuremath sim 10 ensuremath 22 our results are in agreement with zhang s argument stating that the negative tail exponent ensuremath eta d of the asymptotic behavior mathrm ln phantom rule 0 2em 0ex p d e 0 ensuremath sim ensuremath ensuremath mid e 0 ensuremath mid ensuremath eta d as e 0 ensuremath rightarrow ensuremath ensuremath infty is directly related to the fluctuation exponent ensuremath theta d which governs the fluctuations ensuremath delta e 0 l ensuremath sim l ensuremath theta d of the ground state energy e 0 for polymers of length l via the simple formula ensuremath eta d 1 1 ensuremath ensuremath theta d throughout the paper we comment on the similarities and differences with spin glasses

coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces abstract the purpose of this paper is to establish a coupled coincidence point for a pair of commuting mappings in partially ordered complete metric spaces we also present a result on the existence and uniqueness of coupled common fixed points an example is given to support the usability of our results

on ψ φ weakly contractive condition in partially ordered metric spaces recently heman kumar nashine and bessem samet h k nashine b samet fixed point results for mappings satisfying j f weakly contractive condition in partially ordered metric spaces nonlinear anal 74 2011 2201 2209 studied some coincidence fixed point and common fixed point theorems for two mappings satisfying j f weakly contractive condition in an ordered complete metric space in the present paper we study some coincidence fixed point and common fixed point theorems for three mappings s t and r satisfying j f weakly contractive condition in an ordered complete metric space where the mappings s and t are assumed to be weakly increasing with respect to r our results generalize several well known results in the literature

fixed points of multivalued operators in ordered metric spaces with applications abstract the purpose of this paper is to present some new hybrid fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space an example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

positive solutions for a class of singular fractional boundary value problems in this paper we investigate the existence and uniqueness of positive solutions for the following singular fractional boundary value problem d 0 au t f t u t 0 0 0 f t i e f is singular at t 0 our analysis relies on a fixed point theorem in partially ordered sets

the contraction principle for set valued mappings on a metric space with a graph let x d be a metric space and f x x be a set valued mapping we obtain sufficient conditions for the existence of a fixed point of the mapping f in the metric space x endowed with a graph g such that the set v g of vertices of g coincides with x and the set of edges of g is e g x y x y xxx

exact solution for the kardar parisi zhang equation with flat initial conditions we provide the first exact calculation of the height distribution at arbitrary time t of the continuum kardar parisi zhang kpz growth equation in one dimension with flat initial conditions we use the mapping onto a directed polymer with one end fixed one free and the bethe ansatz for the replicated attractive boson model we obtain the generating function of the moments of the directed polymer partition sum as a fredholm pfaffian our formula valid for all times exhibits convergence of the free energy i e kpz height distribution to the gaussian orthogonal ensemble tracy widom distribution at large time

fixed point theorems for generalized contractions in partially ordered metric spaces with semi monotone metric abstract in this paper we study the existence and uniqueness of coupled fixed points for mixed monotone mappings in partially ordered metric spaces with semi monotone metric as an application we prove the existence and uniqueness of the solution for a first order differential equation with periodic boundary conditions

the poorman s transform approximating the fourier transform without multiplication a time domain to frequency domain transformation for sampled signals which is computed with only additions and trivial complex multiplications is described this poorman s transform is an approximation to the usual fourier transform obtained by quantizing the fourier coefficients to the four values or 1 or j and is especially useful when multiplication is expensive for the general case of an n point quantization an analytic formula is given for the error in the approximation which involves only contributions from aliased harmonics continuous time signals are considered in this case the approximation is exact for bandlimited signals

mode coupling and renormalization group results for the noisy burgers equation we investigate the noisy burgers equation kardar parisi zhang equation in 1 1 dimensions using the dynamical renormalization group to two loop order and mode coupling techniques the roughness and dynamic exponent are fixed by galilean invariance and a fluctuation dissipation theorem the fact that there are no singular two loop contributions to the two point vertex functions supports the mode coupling approach which can be understood as a self consistent one loop theory where vertex corrections are neglected therefore the numerical solution of the mode coupling equations yields very accurate results for the scaling functions in addition finite size effects can be studied furthermore the results from exact ward identities as well as from second order perturbation theory permit the quantitative evaluation of the vertex corrections and thus provide a quantitative test for the mode coupling approach it is found that the vertex corrections themselves are of the order 1 surprisingly however their effect on the correlation function is substantially smaller

on the equivalence between a minimal codomain cardinality riesz basis construction a system of hadamard sylvester operators and a class of sparse binary optimization problems piecewise low order polynomial riesz basis families are constructed such that they share the same coefficient functionals of smoother orthonormal bases in a localized indexing subset it is shown that a minimal cardinality basis codomain can be realized by inducing sparsity via l1 regularization in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optimization over a suitably large dictionary furthermore it is shown that a subset of these solutions are equivalent to a specific constrained analytical solution derived via sylvester type hadamard operators

maximum relative height of elastic interfaces in random media the distribution of the maximal relative height mrh of self affine one dimensional elastic interfaces in a random potential is studied we analyze the ground state configuration at zero driving force and the critical configuration exactly at the depinning threshold both for the random manifold and random periodic universality classes these configurations are sampled by exact numerical methods and their mrh distributions are compared with those with the same roughness exponent and boundary conditions but produced by independent fourier modes with normally distributed amplitudes using pickands theorem we derive an exact analytical description for the right tail of the latter after properly rescaling the mrh distributions we find that corrections from the gaussian independent modes approximation are in general small as previously found for the average width distribution of depinning configurations in the large size limit all corrections are finite except for the ground state in the random periodic class whose mrh distribution becomes for periodic boundary conditions indistinguishable from the airy distribution we find that the mrh distributions are in general sensitive to changes of boundary conditions

steady state scaling function of the 1 1 dimensional single step model the steady state height height correlation function for the 1 1 dimensional single step model is calculated in a large scale monte carlo simulation analysis of the data yields a universal ratio of scaling amplitudes which differs from the value obtained recently from a mode coupling calculation an empirical form for a universal scaling function is also presented

continuum model for radial interface growth abstract a stochastic partial differential equation along the lines of the kardar parisi zhang equation is introduced for the evolution of a growing interface in a radial geometry regular polygon solutions as well as radially symmetric solutions are identified in the deterministic limit the polygon solutions of relevance to on lattice eden growth from a seed in the zero noise limit are unstable in the continuum in favour of the symmetric solutions the asymptotic surface width scaling for stochastic radial interface growth is investigated through numerical simulations and found to be characterized by the same scaling exponent as that for stochastic growth on a substrate

equivalent conditions for generalized contractions on ordered metric spaces abstract we establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane as its application we get that various contractive conditions using the so called altering distance functions coincide with classical ones we consider several classes of mappings both on metric spaces and ordered metric spaces in particular we show that unexpectedly some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by harjani and sadarangani j harjani k sadarangani generalized contractions in partially ordered metric spaces and applications to ordinary differential equations nonlinear anal 72 2010 1188 1197 and amini harandi and emami a amini harandi h emami a fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations nonlinear anal 72 2010 2238 2242 do follow from an earlier result of o regan and petrusel d o regan and a petrusel fixed point theorems for generalized contractions in ordered metric spaces j math anal appl 341 2008 1241 1252

universal fluctuations in kardar parisi zhang growth on one dimensional flat substrates we present a numerical study of the evolution of height distributions hds obtained in interface growth models belonging to the kardar parisi zhang kpz universality class the growth is done on an initially flat substrate the hds obtained for all investigated models are very well fitted by the theoretically predicted gaussian orthogonal ensemble goe distribution the first cumulant has a shift that vanishes as t 1 3 while the cumulants of order 2 n 4 converge to goe as t 2 3 or faster behaviors previously observed in other kpz systems these results yield evidences for the universality of the goe distribution in kpz growth on flat substrates finally we further show that the surfaces are described by the airy 1 process

generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces abstract in this paper we extend the coupled fixed point theorems for mixed monotone operators f x x x obtained in t g bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal 65 7 2006 1379 1393 by significantly weakening the contractive condition involved our technique of proof is essentially different and more natural an example as well as an application to periodic bvp is also given in order to illustrate the effectiveness of our generalizations

generalized contractions in partially ordered metric spaces and applications to ordinary differential equations the purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions we also present some applications to first and second order ordinary differential equations

kardar parisi zhang universality class in 2 1 dimensions universal geometry dependent distributions and finite time corrections the dynamical regimes of models belonging to the kardar parisi zhang kpz universality class are investigated in d 2 1 by extensive simulations considering flat and curved geometries geometry dependent universal distributions different from their tracy widom counterpart in one dimension were found distributions exhibit finite time corrections hallmarked by a shift in the mean decaying as t where is the growth exponent our results support a generalization of the ansatz h v t t t to higher dimensions where v and are nonuniversal quantities whereas and are universal and the last one depends on the surface geometry generalized gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak which can be used for comparisons with experiments our numerical results call for analytical approaches and experimental realizations of the kpz class in two dimensional systems

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

coupled fixed point theorems for mixed monotone mappings and an application to integral equations in this paper we extend the coupled fixed point theorems for a mixed monotone mapping f xxx x in partially ordered metric spaces established by bhaskar and lakshmikantham t gnana bhaskar v lakshmikantham fixed point theorems in partially ordered metric spaces and applications nonlinear anal tma 65 2006 1379 1393 an application to nonlinear integral equations is also given to illustrate our results

fixed point theorems for α ψ contractive type mappings abstract in this paper we introduce a new concept of contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces starting from the banach contraction principle the presented theorems extend generalize and improve many existing results in the literature moreover some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results

two loop renormalization group analysis of the burgers kardar parisi zhang equation a systematic analysis of the burgers kardar parisi zhang equation in d 1 dimensions by dynamic renormalization group theory is described the fixed points and exponents are calculated to two loop order we use the dimensional regularization scheme carefully keeping the full d dependence originating from the angular parts of the loop integrals for dimensions less than mathit d mathit c 2 we find a strong coupling fixed point which diverges at d 2 indicating that there is nonperturbative strong coupling behavior for all d ensuremath ge 2 at d 1 our method yields the identical fixed point as in the one loop approximation and the two loop contributions to the scaling functions are nonsingular for dg2 dimensions there is no finite strong coupling fixed point in the framework of a 2 ensuremath epsilon expansion we find the dynamic exponent corresponding to the unstable fixed point which described the nonequilibrium roughening transition to be z 2 o mathrm ensuremath epsilon 3 in agreement with a recent scaling argument by doty and kosterlitz phys rev lett 69 1979 1992 similarly our result for the correlation length exponent at the transition is 1 ensuremath nu ensuremath epsilon o mathrm ensuremath epsilon 3 for the smooth phase some aspects of the crossover from gaussian to critical behavior are discussed

minimal path on the hierarchical diamond lattice we consider the minimal paths on a hierarchical diamond lattice where bonds are assigned a random weight depending on the initial distribution of weights we find all possible asymptotic scaling properties the different cases found are the small disorder case the analog of levy s distributions with a power law decay at and finally a limit of large disorder which can be identified as a percolation problem the asymptotic shape of the stable distributions of weights of the minimal path are obtained as well as their scaling properties as a side result we obtain the asymptotic form of the distribution of effective percolation thresholds for finite size hierarchical lattices

a fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations we present a fixed point theorem for generalized contraction in partially ordered complete metric spaces as an application we give an existence and uniqueness for the solution of a periodic boundary value problem

new fixed point results for maps satisfying implicit relations on ordered metric spaces and application we give some fixed point results for one and two mappings satisfying an implicit relation involving control function on ordered complete metric spaces we furnish suitable examples to demonstrate the validity of the hypotheses of our results we also give an application of our results to nonlinear volterra integro differential equations

a kpz cocktail shaken not stirred the stochastic partial differential equation proposed nearly three decades ago by kardar parisi and zhang kpz continues to inspire intrigue and confound its many admirers here we i pay debts to heroic predecessors ii highlight additional experimentally relevant aspects of the recently solved 1 1 kpz problem iii use an expanding substrates formalism to gain access to the 3d radial kpz equation and lastly iv examining extremal paths on disordered hierarchical lattices set our gaze upon the fate of d infty kpz clearly there remains ample unexplored territory within the realm of kpz and for the hearty much work to be done especially in higher dimensions where numerical and renormalization group methods are providing a deeper understanding of this iconic equation

multisurface coding simulations of the restricted solid on solid model in four dimensions we study the restricted solid on solid model for surface growth in spatial dimension d 4 by means of a multisurface coding technique that allows us to analyze samples of size up to 256 4 in the steady state regime for such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations a careful finite size scaling analysis of the critical exponents clearly indicate that d 4 is not the upper critical dimension of the model

fixed point theorems in partially ordered metric spaces and applications abstract we prove a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order using a weak contractivity type of assumption besides including several recent developments our theorem can be used to investigate a large class of problems as an application we discuss the existence and uniqueness of solution for a periodic boundary value problem

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

maximal height statistics for 1 f alpha signals numerical and analytical results are presented for the maximal relative height distribution of stationary periodic gaussian signals one dimensional interfaces displaying a 1 f alpha power spectrum for 0 1 regime of strong correlations and a highly accurate picture gallery of distribution functions can be constructed numerically analytical results can be obtained in the limit alpha infinity and for large alpha by perturbation expansion furthermore using path integral techniques we derive a trace formula for the distribution function valid for alpha 2n even integer from the latter we extract the small argument asymptote of the distribution function whose analytic continuation to arbitrary alpha 1 is found to be in agreement with simulations comparison of the extreme and roughness statistics of the interfaces reveals similarities in both the small and large argument asymptotes of the distribution functions

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process

common fixed point theorems of gregus type for weakly compatible mappings satisfying generalized contractive conditions abstract we prove a common fixed point theorem of gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of i altun d turkoglu b e rhoades fixed points of weakly compatible mappings satisfying a general contractive condition of integral type fixed point theory appl 2007 2007 article id 17301 a djoudi l nisse gregus type fixed points for weakly compatible mappings bull belg math soc 10 2003 369 378 a djoudi a aliouche common fixed point theorems of gregus type for weakly compatible mappings satisfying contractive conditions of integral type j math anal appl 329 1 2007 31 45 p vijayaraju b e rhoades r mohanraj a fixed point theorem for a pair of maps satisfying a general contractive condition of integral type int j math math sci 15 2005 2359 2364 x zhang common fixed point theorems for some new generalized contractive type mappings j math anal appl 333 2 2007 780 786 we prove also a common fixed point theorem which generalizes theorem 3 5 of h k pathak m s khan t rakesh a common fixed point theorem and its application to nonlinear integral equations comput math appl 53 2007 961 971 and common fixed point theorems of gregus type using a strict generalized contractive condition a property e a and a common property e a