solutions of nonlinear dirac equations abstract we study the dirac equation i t i c k 1 3 k k m c 2 g x and obtain existence and multiplicity results of stationary solutions for several classes of nonlinearities g r 3 c 4 r modeling various types of interaction a typical result states that if g x u depends periodically on x and is even in u the problem has infinitely many geometrically different localized solutions the arguments are variational the associated lagrangian functional is strongly indefinite and the palais smale condition does not hold we apply some recently developed critical point theorems

nodal type bound states of schrodinger equations via invariant set and minimax methods for nonlinear schrodinger equations in the entire space we present new results on invariant sets of the gradient flows of the corresponding variational functionals the structure of the invariant sets will be built into minimax procedures to construct nodal type bound state solutions of nonlinear schrodinger type equations 2004 elsevier inc all rights reserved

critical behavior of the one dimensional diffusive pair contact process the phase transition of the one dimensional diffusive pair contact process is investigated by n cluster mean field approximations and high precision simulations the n 3 4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate d with beta 2 2 mean field order parameter exponent of the pair density this contradicts with former n 2 results where two different mean field behavior was found along the transition line extensive dynamical simulations on l 10 5 lattices give estimates for the order parameter exponents of the particles for 0 05 or d or 0 7 these data may support former two distinct class findings however the gap between low and high d exponents is narrower than previously estimated and the possibility for interpreting numerical data as a single class behavior with exponents alpha 0 21 1 beta 0 40 1 assuming logarithmic corrections is shown finite size scaling results are also presented

compact parity conserving percolation in one dimension compact directed percolation is known to appear at the endpoint of the directed percolation critical line of the domany kinzel cellular automaton in 1 1 dimension equivalently such transition occurs at zero temperature in a magnetic field h upon changing the sign of h in the one dimensional glauber ising model with well known exponents characterizing spin cluster growth we have investigated here numerically these exponents in the non equilibrium generalization of the glauber model in the vicinity of the parity conserving phase transition point of the kinks critical fluctuations on the level of kinks are found to affect drastically the characteristic exponents of spreading of spins while the hyperscaling relation holds in its form appropriate for compact clusters

cloud rain predator prey interactions analyzing some propertiesof the koren feingold model and introduction of a new species competition bulk system with a hopf bifurcation abstract this paper deals with some properties of predator prey cloud rain models focus is put on scaling and on some mathematical features such as stability and limit cycles precisely the koren feingold delay differential equation model is first investigated and it is shown that it has no limit cycles then by considering another point of view i e species competition dynamics for parametrizing cloud rain processes a system of ordinary differential equations to model these processes is formulated some examples are given to illustrate that this model reproduces in a realistic way the essential macroscopic behavior of a cloud rain system the model has a hopf bifurcation at which certain properties of cloud rain interactions in the model are represented this is an important point to prepare for further examination of cloud synchronization in a cloud field by kuramoto model for instance

measurement of returns to scale using a non radial dea model a range adjusted measure approach abstract this research theoretically explores the measurement of returns to scale rts using a non radial dea data envelopment analysis model a range adjusted measure ram is used as a representative of such non radial models historically a type of rts has been discussed within an analytical framework of radial models the radial based rts measurement is replaced by the non radial ram rts measurement in this study when discussing the non radial ram rts measurement this study finds a problem of multiple projections that cannot be found in the radial measurement in this research a new linear programming approach is proposed to identify all efficient dmus decision making units on a reference set the important feature of the proposed approach is that it can deal with a simultaneous occurrence of a multiple reference sets b multiple supporting hyperplanes and c multiple projections all of the three difficulties are handled by the proposed ram rts measurement in particular we discuss both when the three different types of multiple solutions occur on the ram rts measurement and how to deal with such difficulties our research results make it possible to measure not only the type of rts but also the magnitude of rts in the ram measurement

solutions of a nonlinear dirac equation with external fields we study the stationary dirac equation ic hbar sum 3 k 1 alpha k partial k u mc 2 beta u m x u r u x u where m x is a matrix potential describing the external field and r x u stands for an asymptotically quadratic nonlinearity modeling various types of interaction without any periodicity assumption for fixed our discussion includes the coulomb potential as a special case and for the semiclassical situation 0 we handle the scalar fields we obtain existence and multiplicity results of stationary solutions via critical point theory

directed compact percolation cluster size and hyperscaling exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice the corresponding relation for the moment generating function of the length distribution is obtained in closed form whereas in the case of the size distribution only the first three moments are obtained the work is carried out for clusters grown from a seed of arbitrary width on an anisotropic lattice a duality property is shown to exist which relates the moment generating functions on the two sides of the critical curve the moments of both distributions have critical exponents which satisfy a constant gap hypothesis with gap exponents nu 2 and delta 3 corresponding to the scaling length and scaling size respectively the usual hyperscaling relation for directed percolation is found to be invalid for compact clusters and is replaced by delta nu d nu perpendicular to where nu perpendicular to is the exponent corresponding to the cluster width and d is the number of transverse dimensions 1 for the square lattice

convex input and output projections of nonconvex production possibility sets in this paper we characterize the smallest production possibility set that contains a specified set of input output combinations in accordance with neoclassical production economics this possibility set has convex projections into the input and output spaces convex isoquants and it satisfies the assumption of free disposability we obtain it by means of a possibly infinite recursion which builds the possibility set as an ever larger union of convex sets we remark on the nature of the approximations obtained by truncating the recursion and we obtain a necessary and sufficient condition checkable in one iteration for the recursion to stop in the next for the case in which the recursion stops we provide a succinct characterization of the dominance relations among the constituent sets produced by the procedure finally we present examples of both finite and infinite cases the example for the finite case illustrates the construction of the possibility set along with its associated production and consumption sets

generalized scaling relations for unidirectionally coupled nonequilibrium systems abstract unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point we find that for initial conditions with isolated particles each hierarchy level exhibits an inhomogeneous active region coupled and uncoupled respectively the particle number of each level increases algebraically in time as n t t with different exponents in each domain this inhomogeneity is a quite general feature of unidirectionally coupled systems and leads to two hyperscaling relations between dynamic and static critical exponents using the contact process and the branching annihilating random walk with two offsprings which belong to the directed percolation and parity conserving classes respectively we numerically confirm the scaling relations

one dimensional generalized branching annihilating random walker process with stochastic generation of offsprings abstract we introduce a branching annihilating random walker process with two species particles a and b which diffuse creating new particles and annihilating instantaneously a b 0 when they meet each kind of particle branches stochastically having offsprings of the same or different type the model is defined and studied by means of epidemic simulations in a one dimensional discrete lattice the phase diagram of the model exhibits two states the vacuum and the active one separated by a critical line along that line the system undergoes irreversible second order phase transitions monte carlo results show that the transitions belong to the same universality class as directed percolation in the limiting case when the generation of offsprings is forbidden the model is mapped into the standard diffusion limited reaction a b 0 which asymptotically evolves towards the vacuum state the transition between the stationary regime and such vacuum states is also studied

technical efficiency estimation with multiple inputs and multiple outputs using regression analysis regression and linear programming provide the basis for popular techniques for estimating technical efficiency regression based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error in contrast linear programming models are nonparametric and allow multiple inputs and outputs the purported disadvantage of the regression based models is the inability to allow multiple outputs without additional data on input prices in this paper deterministic cross sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed notably technical efficiency can be estimated using regression models characterized by multiple input multiple output environments without input price data we provide multiple examples including a monte carlo analysis

multiple solutions for a semiclassical schrodinger equation abstract this paper is concerned with the semiclassical nonlinear schrodinger equation e 2 u v x u f x u x r n u x 0 as x where e 0 is a small parameter under certain hypotheses on v and a general spectral assumption the existence and multiplicity of semiclassical solutions are obtained for asymptotically linear nonlinearity via variational methods

critical exponents for branching annihilating random walks with an even number of offspring recently takayasu and tretyakov phys rev lett 68 3060 1992 studied branching annihilating random walks baws with n 1 char21 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation in this article i study the baw with n 4 using time dependent simulations and finite size scaling obtaining precise estimates for various critical exponents the results are consistent with the conjecture ensuremath beta ensuremath nu mathrm ensuremath perp 1 2 ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp 7 4 ensuremath gamma 0 ensuremath delta 2 7 ensuremath eta 0 and mathrm ensuremath delta mathit h 9 2 these critical exponents characterize respectively the dependence of the order parameter ensuremath beta ensuremath nu mathrm ensuremath perp and relaxation time ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp on system size the growth of fluctuations ensuremath gamma close to the critical point the long time behavior of the probability of survival ensuremath delta and average number of particles ensuremath eta when starting at time zero with just two particles and finally the decay of the order parameter mathrm ensuremath delta mathit h at the critical point in the presence of an external source

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

bifurcation of steady state solutions in predator prey and competition systems we discuss steady state solutions of systems of semilinear reaction diffusion equations which model situations in which two interacting species u and v inhabit the same bounded region it is easy to find solutions to the systems such that either u or v is identically zero such solutions correspond to the case where one of the species is extinct by using decoupling and global bifurcation theory techniques we prove the existence of solutions which are positive in both u and v corresponding to the case where the populations can co exist

a bi extremal principle for frontier estimation and efficiency evaluations a new approach is supplied for locating efficiency frontiers and evaluating the efficiency of decision making units dmu s this is accomplished from observational data by means of an envelopment procedure called dea data envelopment analysis originally developed by charnes cooper and rhodes charnes a w w cooper e rhodes 1978 measuring the efficiency of decision making units eur j oper res 2 6 see also short communication eur j oper res 3 1979 339 in connection with their ratio formulation for relative efficiency measurement the current variant employs a bi extremal principle which though nonlinear is subsequently shown to be reducible to a finite sequence of linear programming problems the development is illustrated by means of multiple output functions which are piecewise of cobb douglas or general log linear type and which also allow for increasing decreasing and constant returns to scale more than one production function for the dmu s is also allowed the reduction of the bi extremal principle to linear programming equivalence is also accomplished for much more general classes of functions a numerical example illustrates some of these ideas and also provides a springboard for a new theorem which relates these efficiency measures to ones which were supplied earlier in the charnes cooper and rhodes s work charnes a w w cooper e rhodes 1978 measuring the efficiency of decision making units eur j oper res 2 6 see also short communication eur j oper res 3 1979 339

absorbing phase transition in contact process on fractal lattices abstract we investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices i e on a checkerboard fractal and on a sierpinski carpet the checkerboard fractal is finitely ramified with many dead ends while the sierpinski carpet is infinitely ramified we measure various critical exponents of the contact process with a diffusion reaction scheme a aa and a 0 characterized by a spreading with a rate and an annihilation with a rate and the results are confirmed by a crossover scaling and a finite size scaling the exponents compared with the expansion results assuming 4 d f d f being the fractal dimension of the underlying fractal lattice exhibit significant deviations from the analytical results for both the checkerboard fractal and the sierpinski carpet on the other hand the exponents on a checkerboard fractal agree well with the interpolated results of the regular lattice for the fractional dimensionality while those on a sierpinski carpet show marked deviations

nonequilibrium phase transition in a lattice prey predator system abstract we study a lattice model of a prey predator system mean field approximation predicts that the active phase i e one with a finite fraction of preys and predators is a generic phase of this model moreover within this approximation the model exhibits quasi oscillations resembling lotka volterra systems however monte carlo simulations for a one two and three dimensional versions of this model do not support this scenario and predict that at a certain value of some parameter the model enters the absorbing state i e a state where the entire population of predators dies out and the model is invaded by preys simulations for the one dimensional version indicate that the transition into the absorbing state belongs to the directed percolation universality class

crossovers from parity conserving to directed percolation universality the crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean field method in case of models exhibiting z 2 symmetric absorbing phases the cellular automaton version of the nonequilibrium kinetic ising model nekimca and a stochastic cellular automaton invented by grassberger krause and von der twer j phys a 17 l105 1984 the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation dp and the crossover exponent 1 phi approximately equal to 0 53 2 in the case of a branching and annihilating random walk model with an even number of offspring dual to nekimca the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the dp class characterized by the crossover exponent 1 phi approximately equal to 0 205 5 the two different kinds of crossover operators cannot be mapped onto each other and the resulting models show a diversity within the dp universality class in one dimension these subclasses differ in cluster scaling exponents

semiclassical states for nonlinear schrodinger equations with sign changing potentials we establish the existence and multiplicity of semiclassical bound states of the following nonlinear schrodinger equation e2 u v x u g x u for x rn u x 0as x where v changes sign and g is superlinear with critical or supercritical growth as u

simple sandpile model of active absorbing state transitions we study a simple sandpile model of active absorbing state transitions in which a particle can hop out of a site only if the number of particles at that site is above a certain threshold we show that the active phase has product measure whereas nontrivial correlations are found numerically in the absorbing phase it is argued that the system relaxes to the latter phase slower than exponentially the critical behavior of this model is found to be different from that of the other known universality classes

cluster mean field study of the parity conserving phase transition the phase transition of the branching and annihilating random walk with even offspring is studied by n cluster mean field approximations on one dimensional lattices by allowing the system to reach zero branching rate a phase transition can be seen for any n ensuremath leqslant 12 coherent anomaly extrapolations applied for the series of approximations results in ensuremath nu ensuremath perp 1 85 3 and ensuremath beta 0 96 2

epidemic processes with immunization we study a model of directed percolation dp with immunization i e with different probabilities for the first infection and subsequent infections the immunization effect leads to an additional non markovian term in the corresponding field theoretical action we consider immunization as a small perturbation around the dp fixed point in d 6 where the non markovian term is relevant the immunization causes the system to be driven away from the neighborhood of the dp critical point in order to investigate the dynamical critical behavior of the model we consider the limits of low and high first infection rate while the second infection rate remains constant at the dp critical value scaling arguments are applied to obtain an expression for the survival probability in both limits the corresponding exponents are written in terms of the critical exponents for ordinary dp and dp with a wall we find that the survival probability does not obey a power law behavior decaying instead as a stretched exponential in the low first infection probability limit and to a constant in the high first infection probability limit the theoretical predictions are confirmed by optimized numerical simulations in i 1 dimensions

choosing weights from alternative optimal solutions of dual multiplier models in dea in this paper we propose a two step procedure to be used for the selection of the weights that we obtain from the multiplier model in a dea efficiency analysis it is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and consequently have alternate optima for the weights different optimal weights may then be obtained depending for instance on the software used the idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights the selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and in particular it selects those weights associated with a full dimensional efficient facet fdef if any in this sense the weights provided by our procedure will have the maximum support from the production possibility set we also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article

phase structure of systems with infinite numbers of absorbing states critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied we analyze a non markovian langevin equation recently proposed to describe the critical behavior of such systems and also introduce and study a non markovian discrete model which is argued to present the same critical features on the basis of mean field analysis monte carlo simulations and theoretical arguments we conclude that the phenomenology of the non markovian models closely parallels that of systems with many absorbing states in one and two dimensions the bulk or static critical properties of these systems fall in the directed percolation dp universality class by contrast the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior depending on parameter values they can both in one and two dimensions fall either in the dynamical percolation or dp universality class or else exhibit apparently nonuniversal exponents in contrast to previous results however the nonuniversal exponents in 2d are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes dp values these results demonstrate the efficacy of the non markovian approach for understanding systems with many absorbing states which are difficult to analyze in their original microscopic formulation

boundary effects on population dynamics in stochastic lattice lotka volterra models abstract we investigate spatially inhomogeneous versions of the stochastic lotka volterra model for predator prey competition and coexistence by means of monte carlo simulations on a two dimensional lattice with periodic boundary conditions to study boundary effects for this paradigmatic population dynamics system we employ a simulation domain split into two patches upon setting the predation rates at two distinct values one half of the system resides in an absorbing state where only the prey survives while the other half attains a stable coexistence state wherein both species remain active at the domain boundary we observe a marked enhancement of the predator population density the predator correlation length displays a minimum at the boundary before reaching its asymptotic constant value deep in the active region the frequency of the population oscillations appears only very weakly affected by the existence of two distinct domains in contrast to their attenuation rate which assumes its largest value there we also observe that boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern with two different reaction rates assigned to neighboring patches when the domain size becomes reduced to the scale of the correlation length the mean population densities attain values that are very similar to those in a disordered system with randomly assigned reaction rates drawn from a bimodal distribution

dea on relaxed convexity assumptions in a recent paper petersen petersen n c 1990 data envelopment analysis on a relaxed set of assumptions management sci 36 305 314 proposed to relax the convexity assumptions invoked in traditional data envelopment analysis dea unfortunately the new approach is not consistent with the relaxed assumptions also the efficiency evaluations in input and output spaces are based on different technologies assumptions the aim of this paper is to clarify which assumptions are actually involved and to develop modifications such that the input and output based measures are consistent in effect a family of dea methods based on relaxed convexity assumptions is identified

dynamics of gompertzian tumour growth under environmental fluctuations abstract we investigate the effect of correlated additive and multiplicative gaussian white noise on the gompertzian growth of tumours our results are obtained by solving numerically the time dependent fokker planck equation fpe associated with the stochastic dynamics in our numerical approach we have adopted b spline functions as a truncated basis to expand the approximated eigenfunctions the eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study we perform simulations to analyze various aspects of the probability distribution of the tumour cell populations in the transient and steady state regimes more precisely we are concerned mainly with the behaviour of the relaxation time to the steady state distribution as a function of i of the correlation strength between the additive noise and the multiplicative noise and ii as a function of the multiplicative noise intensity d and additive noise intensity it is observed that both the correlation strength and the intensities of additive and multiplicative noise affect the relaxation time

critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder a stochastic cellular automaton exhibiting a parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model this opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state for very strong disorder the model breaks up into blocks with exponential size distribution and continuously changing critical exponents are observed for strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model in which residual particles survive the extinction the critical dynamical behavior of this transition has been explored

spreading analysis and finite size scaling study of the critical behavior of a forest fire model with immune trees abstract in a forest fire model with immune trees ffmit recently proposed by drossel and schwabl physica a 199 1993 183 the sites of the lattice are either empty a tree or a burning tree and at each time step the system is updated in parallel according to the following rules i a burning tree becomes an empty site ii trees grow with probability p from empty sites and iii a green tree becomes a burning tree with probability 1 g if at least one next neighbor is burning fixing an arbitrary grow probability p and starting with a small immunity g increments of g causes the fire density of the steady state to decrease until the fire becomes irreversibly extinguished at a certain critical point of coordinates pc gc the set of critical points defines a critical curve gc p which in the l limit divides the p g plane in two regions a steady state with fire fronts for g

phase diagram of a model of self organizing hierarchies abstract we introduce a simple model of self organizing hierarchies in animal societies which relies on a basic positive feedback mechanism reinforcing the ability of a given individual to win or lose in a hierarchical interaction depending on how many times it won or lost in previous interactions if a forgetting strength is included which determines the rate at which events in the past are forgotten and no longer influence the force of an individual subcritical or supercritical bifurcations in the formation of the hierarchical structure are observed as the density of individuals is varied the nature of the transition is shown to depend on a parameter analogous to the inverse of a temperature defining the amount of determinism in the outcomes of the fights we therefore observe a dynamical tricritical point in the plane

universality split in absorbing phase transition with conserved field on fractal lattices the universality split in absorbing phase transition between the conserved lattice gas clg model and the conserved threshold transfer process cttp is investigated on a checkerboard fractal and on a sierpinski gasket the critical exponents theta beta nu and z which are associated with respectively the density of active particles in time the order parameter the temporal correlation length and the dynamics of active particles are elaborately measured for two models on selected fractal lattices the exponents for the clg model are found to be distinctly different from those of the cttp model on a checkerboard fractal whereas the two models exhibit the same critical behavior on a sierpinski gasket indicating that the universality split between the two models occurs only on a checkerboard fractal such a universality split is attributed from the dominant hopping mechanisms caused by the intrinsic properties of the underlying fractal lattice

a discussion of testing dmus returns to scale abstract the issue of using banker s most productive scale size mpss concept to characterize dmus returns to scale rts is studied in this paper it is shown that the mpss concept can always be used to estimate rts without any adjustments unless a set of efficient dmus exhibit linear dependency i e it is the dmu itself that causes the mpss concept not to work the mpss concept itself is independent of assuming a linear production function in the ccr model as a result chang and ghu s conclusions are erroneous also several other errors in chang and ghu s proof and illustration of proof are listed the linear dependency condition in the current paper corresponds to the nonunique lambda solution situation in banker and thrall meanwhile a remedy is developed for the mpss concept so that it can still work under linear dependency it is also shown that those dmus which naturally exhibit increasing and decreasing returns to scale have nothing to do with linear dependency

existence and multiplicity of semiclassical solutions for a schrodinger equation abstract we establish the existence and multiplicity of solutions for the semiclassical nonlinear schrodinger equation e 2 u v x u g x u for x r n u x 0 as x where e 0 is a small parameter and the potential v changes sign and may not be bounded from below and g x u is asymptotically linear in u as u

infinite numbers of absorbing states critical behavior we briefly review recent progress in elucidating the time independent critical behavior of systems with infinite numbers of static absorbing states and show that the critical exponent describing the decay with time of the order parameter right at the critical point is the same as that of the directed percolation problem

interval efficiency measures in data envelopment analysis with imprecise data the conventional data envelopment analysis dea measures the relative efficiencies of a set of decision making units dmus with exact values of inputs and outputs for imprecise data i e mixtures of interval data and ordinal data some methods have been developed to calculate the upper bound of the efficiency scores this paper constructs a pair of two level mathematical programming models whose objective values represent the lower bound and upper bound of the efficiency scores respectively based on the concept of productive efficiency and the application of a variable substitution technique the pair of two level nonlinear programs is transformed to a pair of ordinary one level linear programs solving the associated pairs of linear programs produces the efficiency intervals of all dmus an illustrative example verifies the idea of this paper a real case is also provided to give some interpretation of the interval efficiency interval efficiency not only describes the real situation in better detail psychologically it also eases the tension of the dmus being evaluated as well as the persons conducting the evaluation

extinction survival and dynamical phase transition of branching annihilating random walk we analyze statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate numerical results for one two and three dimensions and for the sierpinski gasket are assessed in view of the mean field theory predictions universality classes are found to depend on the number of offsprings in space dimension less than 3

phase transition between synchronous and asynchronous updating algorithms we update a one dimensional chain of ising spins of length l with algorithms which are parameterized by the probability p for a certain site to get updated in one time step the result of the update event itself is determined by the energy change due to the local change in the configuration in this way we interpolate between the metropolis algorithm at zero temperature when p is of the order of 1 l and l is large and a synchronous deterministic updating procedure for p 1 as a function of p we observe a phase transition between the stationary states to which the algorithm drives the system these are non absorbing stationary states with antiferromagnetic domains for p p c and absorbing states with ferromagnetic domains for p p c this means that above this transition the stationary states have lost any remnants of the ferromagnetic ising interaction a measurement of the critical exponents shows that this transition belongs to the universality class of parity conservation

linear production functions and the data envelopment analysis abstract this paper shows that the data envelopment analysis or farrell method is not nonparametric in the sense that the method implicitly employs linear production functions frontiers to measure efficiency deriving positive multiplier linear production frontiers and grouping the dmus by their corresponding frontiers can simplify the estimation procedures when there are new dmus included and can easily determine how many inputs should be reduced or and how many outputs should be increased to make an inefficient dmu efficiently this procedure can also circumvent the problems of the non archimedean infinitesmal in the ccr literature it is also shown that because of the linear production functions both banker s and the banker charnes cooper methods fail in testing for returns to scale

on piecewise reference technologies in this paper we introduce a piecewise parametric production model that may be used as a reference technology for efficiency gauging we show that other piecewise reference technologies used in efficiency measuring are obtained as special cases of our model

on the oscillatory dynamical behaviour of epidemic spreading in fractal media we present numerical evidence that dynamical physical processes that develop a time dependent characteristic length and take place in fractal media exhibiting spatial discrete scale invariance dsi with fundamental scaling ratio b may become coupled to the topology of the fractal leading to the observation of time dsi the hallmark of time dsi is the observation of a log periodic modulation of the dynamic or kinetic observables which is characterized by a well defined fundamental time scaling ratio both fundamental scaling ratios are linked according to b 1 z where z is the dynamic exponent characteristic of the physical process specifically we have studied the epidemic behaviour of the contact process cp in sierpinski carpets the cp exhibits second order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility we observed that relevant dynamic observables such as the number of active sites the survival probability of the epidemics and the mean square displacement of the epidemic from the origin r2 t exhibit log periodic modulations by fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents since at criticality one has that r2 t t2 z an independent estimation of the dynamic exponent can be performed in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and

homoclinic orbits for a nonperiodic hamiltonian system abstract in this paper we prove the existence and multiplicity of homoclinic orbits for first order hamiltonian systems of the form z j h z t z where h z is asymptotically linear at and is not assumed to be periodic

absorbing phase transition in conserved lattice gas model on fractal lattices we study the continuous phase transition of the conserved lattice gas clg model from an active phase into an absorbing phase on two fractal lattices i e on a checkerboard fractal and on a sierpinski gasket in the clg model a particle is assumed to be active if any of the neighboring sites are occupied by a particle and inactive if all neighboring sites are empty we estimate critical exponents theta beta nu and nu perpendicular characterizing respectively the density of active particles in time the order parameter the temporal and spatial correlation lengths near the critical point and the results are confirmed by off critical scaling and finite size scaling the order parameter exponent beta on a checkerboard fractal appears to lie between the one dimensional 1d value and two dimensional 2d value of the clg model while that on a sierpinski gasket lies between the 1d and 2d values of the conserved threshold transfer process such a difference is manifested based on the intrinsic properties of the underlying fractal lattices

homoclinic orbits for asymptotically linear hamiltonian systems we study the existence of homoclinic orbits for first order time dependent hamiltonian systems z jhz z t where h z t depends periodically on t and hz z t is asymptotically linear in z as z we also consider an asymptotically linear schrodinger equation in rn

the measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane this research theoretically explores the measurement of rts returns to scale under a possible occurrence of multiple solutions in dea data envelopment analysis in this study the occurrence of multiple solutions is classified into type i and type ii type i is an occurrence of multiple solutions in a reference set type ii is an occurrence of multiple solutions on a supporting hyperplane passing on the reference set both types i and ii are very well known among dea researchers but previous research has not sufficiently explored a simultaneous occurrence of type i and type ii in the rts measurement the two types of multiple solutions influence a degree of rts in the dea measurement such a quantitative issue on rts is examined from the perspective of the type i and type ii problems to deal with such difficulties a new linear programming approach is proposed to identify all efficient dmus decision making units that consist of a reference set even if multiple solutions occur on the reference set based upon the research result we can identify when multiple solutions of type i and or type ii occur on the rts measurement and how to deal with such difficulties our research result makes it possible to measure a degree of scale economies rts under the simultaneous occurrence of type i and type ii

branching annihilating random walks in one dimension some exact results we derive a self duality relation for a one dimensional model of branching and annihilating random walkers with an even number of offspring on nearest neighbour sites with the duality relation and by deriving further exact results in some limiting cases involving fast diffusion we obtain new information on the location and nature of the phase transition line between an active stationary state non zero density and an absorbing state extinction of all particles thus clarifying some so far open problems in these limits the transition is mean field like but on the active side of the phase transition line the fluctuation in the number of particles deviates from its mean field value we also show that well within the active region of the phase diagram a finite system approaches the absorbing state very slowly on a time scale which diverges exponentially in system size in the absence of particle diffusion the branching process with infinite annihilation rate is strongly non ergodic

largest size efficient scale and size efficiencies of decision making units in data envelopment analysis abstract this paper extends the usual dea analysis which evaluates input savings that could have been effected by a decision making unit given its observed task to inquire into whether even greater savings would be possible if the task were to be optimally apportioned to a number of smaller units the notion of size efficiency is introduced to measure this potential for further input reductions and then compared and contrasted to the extant notion of scale efficiency the existence of a largest radially size efficient output scale is established as a ray property of the production frontier an illustrative application to hospitals is described

splitting the voter potts model critical point recently some two dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class we show that for an absorbing states potts model with finite but further than nearest neighbor range of interactions the critical point is split into two critical points one of the ising type and the other of the directed percolation universality class similar splitting takes place in the three dimensional nearest neighbor model

critical edge between frozen extinction and chaotic life the cellular automata game of life gl proposed by j conway simulates the dynamic evolution of a society of living organisms it has been extensively studied in order to understand the emergence of complexity and diversity from a set of local rules more recently the capability of gl to self oranize into a critical state has opened an interesting debate in this work we adopt a different approach by introducing stochastic rules in the gl it is found that life exhibits a very rich critical behavior discontinuous first order irreversible phase transitions ipt s between an extinct phase and a steady state supporting life are found a precise location of the critical edge is achieved by means of an epidemic analysis which also allows us to determine dynamic critical exponents furthermore by means of a damage spreading study we conclude that the living phase is chaotic the edge of the frozen chaotic transition coincides with that of the ipt s life extinction close to the edge fractal spreading of the damage is observed however deep inside the living phase such spreading becomes homogeneous c 1995 the american physical society

series expansions for the percolation probability of a generalized domany kinzel cellular automaton series expansions have been derived for the percolation probability of a generalized domany kinzel cellular automaton with two equivalent absorbing states the analysis of the series generally yields estimates of the critical exponent consistent with earlier monte carlo studies thus confirming that the model belongs to the same universality class as branching annihilating random walks with an even number of offspring there is evidence to suggest that when the probability of spreading from two active sites becomes small a new critical behaviour emerges

fixation in a cyclic lotka volterra model we study a cyclic lotka volterra model of n interacting species populating a d dimensional lattice in the realm of a kirkwood approximation a critical number of species nc d above which the system fixates is determined analytically we find nc d 5 14 23 in dimensionsdd 1 2 3 in remarkably good agreement with simulation results in two dimensions a cyclic variant of the lotka volterra model of interacting populations originally introduced by vito volterra for the description of the struggle for existence among species 1 2 has then appeared in a number of apparently unrelated fields ranging from plasma physics 3 to integrable systems 4 5 recently the cyclic lotka volterra model also known as the cyclic voter model has attracted considerable interest as it was realized that introduction of the spatial structure drastically enriches the dynamics 6 11 namely if species live on a one dimensional 1d lattice a homogeneous initial state evolves into a coarsening mosaic of interacting species this heterogeneous spatial structure spontaneously develops when the number of species is sufficiently small n nc fixation occurs i e the system approaches a frozen state little is known in higher dimensions not even the existence of nc has yet been established theoretically or numerically in simulations on two dimensional 2d lattices with n 6 10 species no sign of fixation has been found and instead a reactive steady state has been observed 6 11 in this letter we investigate the cyclic lotka volterra model in the framework of a kirkwood like approximation this approach predicts a finite nc in all spatial dimensions in the following we shall use the language of the voter model 12 consider the cyclic voter model with n possible opinions each site of a d dimensional cubic lattice is occupied by a voter which has an opinion labelled by with d 1 n voters can change their opinions in a cyclic manner 1 modulo n according to the opinions of their neighbourhood specifically the following sequential dynamics is implemented i we randomly choose a site of opinion say and one of its 2d nearest neighbours of opinion ii if d 1 then the chosen site changes its opinion from to d 1 and iii otherwise opinion does not change we set the timescale so that in unit time each site of the lattice is chosen once on average when nd 2 the cyclic voter model is

fluctuations and correlations in lattice models for predator prey interaction including spatial structure and stochastic noise invalidates the classical lotka volterra picture of stable regular population cycles emerging in models for predator prey interactions growth limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator prey model variant where the predation process includes next nearest neighbor interactions we find that the corresponding stochastic model reproduces the above scenario in dimensions 1 d or 4 in contrast with the mean field theory which predicts a first order phase transition however the mean field features are recovered upon allowing for nearest neighbor particle exchange processes provided these are sufficiently fast

propagation and extinction in branching annihilating random walks we investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension depending on the branching and annihilation rates a few particle initial state can evolve to a propagating finite density wave or extinction may occur in which the number of particles vanishes in the long time limit the number parity conserving case where 2 offspring are produced in each branching event can be solved exactly for unit reaction probability from which qualitative features of the transition between propagation and extinction as well as intriguing parity specific effects are elucidated an approximate analysis is developed to treat this transition for general baw processes a scaling description suggests that the critical exponents which describe the vanishing of the particle density at the transition are unrelated to those of conventional models such as reggeon field theory p a c s numbers 02 50 s 05 40 j 82 20 w

reaction diffusion processes and non perturbative renormalization group this paper is devoted to investigating non equilibrium phase transitions to an absorbing state which are generically encountered in reaction diffusion processes it is a review based on canet delamotte deloubriere and wschebor 2004 phys rev lett 92 195703 canet chate and delamotte 2004 phys rev lett 92 255703 and canet et al 2005 phys rev lett 95 100601 of recent progress in this field that has been allowed by a non perturbative renormalization group approach we mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non perturbative features and that hence the use of a non perturbative method turns out to be crucial to get a correct picture of the physics of these models

the three species monomer monomer model in the reaction controlled limit we study the one dimensional three species monomer monomer reaction model in the reaction controlled limit using mean field theory and dynamic monte carlo simulations the phase diagram consists of a reactive steady state bordered by three equivalent adsorbing phases where the surface is saturated with one monomer species the transitions from the reactive phase are all continuous while the transitions between adsorbing phases are first order bicritical points occur where the reactive phase simultaneously meets two adsorbing phases the transitions from the reactive to an adsorbing phase show directed percolation critical behaviour while the universal behaviour at the bicritical points is in the even branching annihilating random walk class the results are contrasted and compared with previous results for the adsorption controlled limit of the same model

absorbing state phase transitions with extremal dynamics extremal dynamics represents a path to self organized criticality in which the order parameter is tuned to a value of zero the order parameter is associated with a phase transition to an absorbing state given a process that exhibits a phase transition to an absorbing state we define an extremal absorbing process providing the link to the associated extremal nonabsorbing process stationary properties of the latter correspond to those at the absorbing state phase transition in the former studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible in the case of the bak sneppen bs model the absorbing version is closely related to the f avalanche introduced by paczuski maslov and bak phys rev e 53 414 1996 or in spreading simulations to the bs branching process also studied by these authors the corresponding nonextremal process belongs to the directed percolation universality class we revisit the absorbing bs model obtaining refined estimates for the threshold and critical exponents in one dimension we also study an extremal version of the usual contact process using mean field theory and simulation the extremal condition slows the spread of activity and modifies the critical behavior radically defining an extremal directed percolation universality class of absorbing state phase transitions asymmetric updating is a relevant perturbation for this class even though it is irrelevant for the corresponding nonextremal class

time dependent perturbation theory for diffusive non equilibrium lattice models the authors recently presented a perturbation theory for the asymptotic survival probability of an interacting particle system which can become trapped in an absorbing state they extend the method to a simple diffusive model analysis of the resulting series shows that diffusion is an irrelevant perturbation i e it does not change the critical behaviour quantitative predictions of the phase boundary are confirmed by results of monte carlo simulations

critical behavior of a tumor growth model directed percolation with a mean field flavor we examine the critical behavior of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells our results support the previous report ferreira et al phys rev e 85 010901 r 2012 which suggested that the critical behavior of the model differs from the expected directed percolation dp universality class surprisingly only some of the critical exponents perpendicular and z take non dp values while some others and spreading dynamics exponents z remain very close to their dp counterparts the obtained exponents satisfy the scaling relations and the generalized hyperscaling relation d z where the dynamical exponent z is however used instead of the spreading exponent z both in d 1 and d 2 versions of our model the exponent most likely takes the mean field value 1 and we speculate that it might be due to the roulette wheel selection which is used to choose the site to supply a nutrient

numerical analysis of the rebellious voter model the rebellious voter model introduced by sturm and swart 2008 is a variation of the standard one dimensional voter model in which types that are locally in the minority have an advantage it is related both through duality and through the evolution of its interfaces to a system of branching annihilating random walks that is believed to belong to the parity conservation universality class this paper presents numerical data for the rebellious voter model and for a closely related one sided version of the model both models appear to exhibit a phase transition between noncoexistence and coexistence as the advantage for minority types is increased for the one sided model but not for the original two sided rebellious voter model it appears that the critical point is exactly a half and two important functions of the process are given by simple explicit formulas a fact for which we have no explanation

standing waves with a critical frequency for nonlinear schrodinger equations this paper is concerned with the existence and qualitative property of standing wave solutions for the nonlinear schrodinger equation with e being a critical frequency in the sense that we show that there exists a standing wave which is trapped in a neighbourhood of isolated minimum points of v and whose amplitude goes to 0 as moreover depending upon the local behaviour of the potential function v x near the minimum points the limiting profile of the standing wave solutions will be shown to exhibit quite different characteristic features this is in striking contrast with the non critical frequency case which has been extensively studied in recent years

conservation laws and universality in branching annihilating random walks takayasu and tretyakov 1992 studied branching annihilating random walks with n 1 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo two and the critical behaviour is not compatible with directed percolation branching annihilating random walks with n 4 additional process spontaneous annihilation which breaks the conservation law are studied the inclusion of spontaneous annihilation even at very small rates leads to directed percolation critical behaviour

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

phase transitions in a lattice population model we introduce a model for a population on a lattice with diffusion and birth death according to and for a particle a we find that the model displays a phase transition from an active to an absorbing state which is continuous in 1 1 dimensions and of first order in higher dimensions in agreement with the mean field equation for the 1 1 dimensional case we examine the critical exponents and a scaling function for the survival probability and show that it belongs to the universality class of directed percolation in higher dimensions we look at the first order phase transition by plotting a histogram of the population density and use the presence of phase coexistence to find an accurate value for the critical point in 2 1 dimensions

field theory of branching and annihilating random walks we develop a systematic analytic approach to the problem of branching and annihilating random walks equivalent to the diffusion limited reaction processes 2a and a m 1 a where m 1 starting from the master equation a field theoretic representation of the problem is derived and fluctuation effects are taken into account via diagrammatic and renormalization group methods for d 2 the mean field rate equation which predicts an active phase as soon as the branching process is switched on applies qualitatively for both even and odd m but the behavior in lower dimensions is shown to be quite different for these two cases for even m and d near 2 the active phase still appears immediately but with nontrivial crossover exponents which we compute in an expansion in 2 d and with logarithmic corrections in d 2 however there exists a second critical dimension d c 4 3 below which a nontrivial inactive phase emerges with asymptotic behavior characteristic of the pure annihilation process this is confirmed by an exact calculation in d 1 the subsequent transition to the active phase which represents a new nontrivial dynamic universality class is then investigated within a truncated loop expansion which appears to give a correct qualitative picture the model with m 2 is also generalized to n species of particles which provides yet another universality class and which is exactly solvable in the limit n for odd m we show that the fluctuations of the annihilation process are strong enough to create a nontrivial inactive phase for all d 2 in this case the transition to the active phase is in the directed percolation universality class finally we study the modification when the annihilation reaction is 3a when m 0 mod 3 the system is always in its active phase but with logarithmic crossover corrections for d 1 while the other cases should exhibit a directed percolation transition out of a fluctuation driven inactive phase

a multiplier bound approach to assess relative efficiency in dea without slacks abstract in this paper we propose a new approach to deal with the non zero slacks in data envelopment analysis dea assessments that is based on restricting the multipliers in the dual multiplier formulation of the used dea model it guarantees strictly positive weights which ensures reference points on the pareto efficient frontier and consequently zero slacks we follow a two step procedure which after specifying some weight bounds results in an assurance region type model that will be used in the assessment of the efficiency the specification of these bounds is based on a selection criterion among the optimal solutions for the multipliers of the unbounded dea models that tries to avoid the extreme dissimilarity between the weights that is often found in dea applications the models developed do not have infeasibility problems and we do not have problems with the alternate optima in the choice of weights that is made to use our multiplier bound approach we do not need a priori information about substitutions between inputs and outputs and it is not required the existence of full dimensional efficient facets on the frontier either as is the case of other existing approaches that address this problem

universality of the local persistence exponent for models in the directed ising class in one dimension we investigate local persistence in five different models and their variants in the directed ising di universality class in one dimension these models have right left symmetry we study grassberger s models a and b we also study branching and annihilating random walks with two offspring the nonequilibrium kinetic ising model and the interacting monomer dimer model grassberger s models are updated in parallel this is not the case in other models we find that the local persistence exponent in all these models is unity or very close to it a change in the mode of the update does not change the exponent unless the universality class changes in general persistence exponents are not universal thus it is of interest that the persistence exponent in a range of models in the di class is the same excellent scaling behavior of finite size scaling is obtained using exponents in the di class in all models we also study off critical scaling in some models and di exponents yield excellent scaling behavior we further study graded persistence which shows similar behavior however for a logistic map with delay which also has the transition in the di class there is no transition from nonzero to zero persistence at the critical point thus the accompanying transition in persistence and universality of the persistence exponent hold when the underlying model has right left symmetry