the equivariant ring of conditions of conics abstract in this paper we are going to give an explicit description of the so called ring of conditions of conics i e of the homogenous space pgl 3 pso 3 this is achieved by first describing its equivariant version

the ring of conditions of a semisimple group abstract in this paper we are going to give an explicit description of the so called ring of conditions of an adjoint semisimple algebraic group g originally introduced in c de concini c procesi complete symmetric varieties ii intersection theory in algebraic groups and related topics kyoto nagoya 1983 in adv stud pure math vol 6 north holland amsterdam 1985 pp 481 513 in order to study intersection theory in g

upper bounds for survival probability of the contact process a precise description of the nontrivial upper invariant measure for c is still an open problem for the basic contact process which is a self dual attractive but nonreversible markov process of an interacting particle system by its self duality to identify the invariant measure is equivalent to determining the initial state dependence of the survival probability of the process a procedure to give rigorous upper bounds for the survival probability is presented based on a lemma given by harris two new bounds are given improving the simple branching process bound in the one dimensional case the present procedure can be viewed as a trial to make approximate measures by generalized markov extensions

series expansion for a stochastic sandpile using operator algebra we extend the series for the activity density in a one dimensional stochastic sandpile with fixed particle density p the first terms of which were obtained via perturbation theory dickman and vidigal 2002 j phys a math gen 35 7269 the expansion is in powers of the time the coefficients are polynomials in p we devise an algorithm for evaluating expectations of operator products and extend the series to constructing pade approximants to a suitably transformed series we obtain predictions for the activity that compare well against simulations in the supercritical regime

multiple objective programming with polynomial objectives and constraints abstract an approach to solving multiple objective programming problems with polynomial objectives and polynomial constraints is developed the notions of pre efficient solution and local efficient solution are investigated relative to the single objective problem of benson illustrative examples are presented in which the solutions are obtained by means of homotopy continuation

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

interactive balance space approach for solving multi level multi objective programming problems this paper studies a multi level multi objective decision making ml modm problems with linear or non linear constraints the objective functions at each level are non linear functions which are to be maximized or minimized this paper presents a three level multi objective decision making tl modm model and an interactive algorithm for solving such a model the algorithm simplifies three level multi objective decision making problems by transforming them into separate multi objective decision making problems at each level thereby avoiding the difficulty associated with non convex mathematical programming our algorithm is an extension of the work of shi and xia x shi h xia interactive bi level multi objective decision making journal of the operational research society 48 1997 943 949 which dealt with interactive bi level multi objective decision making problems with some modifications in assigning satisfactoriness to each objective function in all the levels of the tl modm problem also we solve each separate multi objective decision making problem of the tl modm problem by the balance space approach a new formula is introduced to interconnect the satisfactoriness and the proportions of deviation needed to reflect the relative importance of each objective function thus we have the proportions of deviation including satisfactoriness in addition we present new definitions for the satisfactoriness and the preferred solution in view of singular level multi objective decision making problems that corresponds to the h optimal solution of the balance space approach also new definitions for the feasible solution and the preferred solution h optimal point of the tl modm problem are presented an illustrative numerical example is given to demonstrate the algorithm

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

nonconvex optimization for pricing and hedging in imperfect markets the paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions transaction costs are quite general and far from linear or convex the concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems their optimality conditions and solutions yield strategies to invest and hedging portfolios as well as bid ask spread improvements they also point out the role of coalitions when dealing with these markets several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice as well as to measure its effect on the general efficiency of the market all these findings may be especially important for many emerging and still illiquid spot or derivative markets electricity markets commodity markets markets related to weather inflation linked or insurance linked derivatives etc

note finding certain weakly efficient vertices in multiple objective linear fractional programming recently kornbluth and steuer have developed a simplex based algorithm for finding all weakly efficient vertices of an augmented feasible region of a multiple objective linear fractional programming problem as part of this algorithm they presented a method for detecting certain weakly efficient vertices called break points in this note we show that the procedure used by kornbluth and steuer in this method for computing the numbers needed to find these break points may sometimes fail we also propose a fail safe method for computing these numbers and give some computational results with this method

retrieval and use of the balance set in multiobjective global optimization abstract it is shown on examples how to compute the balance set and the balance number in vector optimization problems vops of different nature new developments are presented concerning possible interrelation between the balance set and the balance number a new notion of the projection of the balance set onto the parameter space new approaches for solving vops with unbounded objective functions and some approximation techniques in determining the balance set

experiments with classification based scalarizing functions in interactive multiobjective optimization in multiobjective optimization methods the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways we compare both theoretically and numerically the performance of three classification based scalarizing functions and pay attention to how well they obey the classification information in particular we devote special interest to the differences the scalarizing functions have in the computational cost of guaranteeing pareto optimality it turns out that scalarizing functions with or without so called augmentation terms have significant differences in this respect we also collect a set of mostly nonlinear benchmark test problems that we use in the numerical comparisons

nonlinear multiple objective optimization an algorithm and some theory this paper presents an algorithm and the supporting theory for solving a class of nonlinear multiple criteria optimization problems using zionts wallenius type of interaction the zionts wallenius method as extended in this paper can be used for solving multiple criteria problems with concave objective and implicit value functions and convex feasible regions modifications of the method to handle nonconvex feasible regions and general nonlinear objective functions are also discussed

distributed computation of pareto sets the needs of multidisciplinary engineering design have motivated the development of distributed solution approaches to computing efficient solutions to decomposable multiobjective optimization problems mops the decomposition is necessary due to the assumption that the overall mop is not solvable since access to its solution space is subproblem restricted the state of the art analyses for distributed solution approaches such as the alternating direction method of multipliers admm and the block coordinate descent bcd method were developed in the context of problem decomposition originating in a single objective setting and are not immediately applicable to mops applying certain scalarization techniques well suited for nonconvex mops the decomposable mop is reformulated into a single objective problem sop but the decomposability is not preserved and the sop is not suitable for the application of admm furthermore coupling between the subproblems makes bcd in its current form likewise inadequate

existence and characterization of efficient decisions with respect to cones existence and characterization theorems for the efficient nondominated set of decisions inr n are presented the existence is proved when the set of decisions satisfies some compactness conditions the efficient set is characterized in terms of the exposed efficient decisions when certain convexity and compactness conditions are satisfied

critical behaviour of a diffusive model with one adsorbing state the authors study the critical behaviour of a nonequilibrium model for adsorption desorption with diffusion they consider a parallel updating rule of the cellular automata type without diffusion it is found that the critical exponents belong to the universality class of directed percolation as has already been shown for sequential dynamics when diffusion is present the critical behaviour can be described in terms of a crossover between the directed percolation regime and a dynamical mean field regime associated with the case of arbitrarily large diffusion

cohomology of regular embeddings we give in this paper an explicit description of the rational cohomology ring of a complete symmetric variety or regular compactification of an algebraic symmetric variety the motivation for this computation comes from the desire to describe an explicit schubert calculus for these varieties which have been considered since the work of chasles and schubert in several special cases the technique we use is the result of our attempts to understand better the work of jurkiewicz and danilov in the case of torus embeddings the combinatorial presentation of the cohomology ring of a smooth torus embedding finds a natural explanation and proof using the language of equivariant cohomology the key point is that the reisner stanley algebra of the torus embedding coincides with its equivariant cohomology ring we consider a class of spaces regular embeddings that contains both complete symmetric varieties and smooth torus embeddings by suitably generalizing the notion of reisner stanley algebra we are able to compute the rational equivariant cohomology ring of these spaces in an explicit way

linear complementarity problems and multiple objective programming an equivalence is demonstrated between solving a linear complementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem a new multiple objective programming based approach to solving linear complementarity problems is presented results on existence uniqueness and computational complexity are included

simplified method for including spatial correlations in mean field approximations biological systems involving proliferation migration and death are observed across all scales for example they govern cellular processes such as wound healing as well as the population dynamics of groups of organisms in this paper we provide a simplified method for correcting mean field approximations of volume excluding birth death movement processes on a regular lattice an initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity depending on the relative rates of proliferation migration and death many frameworks chosen to model these systems neglect spatial correlations which can lead to inaccurate predictions of their behavior for example the logistic model is frequently chosen which is the mean field approximation in this case this mean field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances in this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time we test our simplified model against the more complex corrected mean field model finding excellent agreement we show how our model successfully predicts system behavior in regions where the mean field approximation shows large discrepancies additionally we investigate regions of parameter space where migration is reduced relative to proliferation which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean field model in these parameter regimes

a combined tchebycheff aspiration criterion vector interactive multiobjective programming procedure in this paper we combine the tchebycheff method of steuer and choo with wierzbicki s aspiration criterion vector method in order to form an improved procedure for interactive multiple objective programming the combined procedure is sensible because the tchebycheff and aspiration criterion vector methods possess complementary distinguishing characteristics solve similar optimization problems to probe the nondominated set and share a similar computer user interface in the early iterations tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search in later iterations aspiration criterion vector probes might be used to pinpoint a final solution computational experience is reported showing the improved effectiveness of the combined procedure when employed in this fashion when compared against the tchebycheff and aspiration criterion vector methods run separately

application of the mean field renormalization group to nonequilibrium critical phenomena abstract we present results of an extension of mfrg ideas to some nonequilibrium systems exhibiting a continuous transition to an absorbing state critical parameters are determined for the contact process in one and higher dimensions and for some related models the effects of hopping between neighbours and other changes in the dynamic rules are considered

the balance space approach to multicriteria decision making involving the decision maker abstract the balance space approach introduced by galperin in 1990 provides a new view on multicriteria optimization looking at deviations from global optimality of the different objectives balance points and balance numbers are defined when either different or equal deviations for each objective are allowed apportioned balance numbers allow the specification of proportions among the deviations through this concept the decision maker can be involved in the decision process in this paper we prove that the apportioned balance number can be formulated by a min max operator furthermore we prove some relations between apportioned balance numbers and the balance set and see the representation of balance numbers in the balance set the main results are necessary and sufficient conditions for the balance set to be exhaustive which means that by multiplying a vector of weights proportions of deviation with its corresponding apportioned balance number a balance point is attained the results are used to formulate an interactive procedure for multicriteria optimization all results are illustrated by examples

application of time power series to nonequilibrium critical phenomena abstract we treat the kinetics of a one dimensional lattice gas adsorption model with a critical point we use a matrix method to construct an exact time power series to describe the dynamics inverting the series gives the time as a function of the density in terms of a well behaved density series from which one can derive a set of finite polynomials that give successively improving estimates of the critical parameter from the ratios of successive coefficients in the density series one can estimate the critical exponent for the time dependence of the critical process

nonequilibrium spin models with ising universal behaviour the properties of a family of nonequilibrium spin models with up down symmetry on a square lattice are determined by a mean field pair approximation and by monte carlo simulation the phase diagram in the parameter space displays a critical line that terminates at a first order critical point it is found that the critical exponents are the same as those of the equilibrium ising model

perturbative series expansion for the subcritical stationary properties of the contact process the subcritical stationary properties of the contact process in one dimension are studied by perturbative series expansions in powers of the creation rate to avoid entering the absorbing state and thus obtaining a nonzero stationary distribution of particles three small modifications on the rules of the contact process are considered the series expansions for the average number of particles and the spatial correlation length are analysed by pade approximants from which the values of the critical creation rate and the critical exponents are obtained

field theoretic approach to metastability in the contact process a quantum field theoretic formulation of the dynamics of the contact process on a regular graph of degree z is introduced a perturbative calculation in powers of 1 z of the effective potential for the density of particles phi t and an instantonic field psi t emerging from the quantum formalism is performed corrections to the mean field distribution of densities of particles in the out of equilibrium stationary state are derived in powers of 1 z results for typical e g average density and rare fluctuation e g lifetime of the metastable state properties are in very good agreement with numerical simulations carried out on d dimensional hypercubic z 2d and cayley lattices

on efficient sets in vector maximum problems a brief survey the notion of efficient nondominated noninferior pareto optimal functional efficient set to a vectormaximum problem vmp has been analysed and developed in several directions during the last 30 years starting with the basic notion of efficiency given by pareto 1896 formal descriptions of the efficient properly efficient locally proper efficient weak or strong efficient set have been developed beginning in the 50th of this century based on these notions various characteristics and properties of the efficient set have been studied whereas the feasible set x and the functions zk x k 1 k constituting the vector valued criterion z x of vmp have various properties e g convexity of x concavity of zk x for all k differentiability etc based on such properties the structure of the efficient set and the existence of efficient solutions have been analysed a part of the corresponding publications are rather of a pure theoretical character others try to develope theories serving as the basis for working out methods for determining the efficient set or for interactive methods determining some compromise solutions duality theories for more or less general cases have been developed and various aspects of stability of vmp have been investigated a brief survey is given

min max formulation of the balance number in multiobjective global optimization abstract the notion of the balance number introduced by galperin through a certain set contraction procedure for nonscalarized multiobjective global optimization is represented via a min max operation on the data of the problem this representation yields a different computational procedure for the calculation of the balance number and allows us to generalize the approach for problems with countably many performance criteria comparisons with pareto optimality and compromise solutions are discussed and illustrated by examples it is demonstrated that l p norm scalarizations 1 p

a comparative study for the pair creation contact process using series expansions a comparative study between two distinct perturbative series expansions for the pair creation contact process is presented in contrast to the ordinary contact process whose supercritical series expansions provide accurate estimates for its critical behaviour the supercritical approach does not work properly when applied to the pair creation process to circumvent this problem a procedure is introduced in which one site creation is added to the pair creation an alternative method is the generation of subcritical series expansions which works even for the case of the pure pair creation process in contrast to the supercritical case the subcritical series yields estimates that are compatible with numerical simulations

equivariant cohomology of the wonderful group compactification in this paper we compute the rational g g equivariant cohomology ring of the so called wonderful compactification of g see c de concini c procesi complete symmetric varieties in invariant theory montecatini 1982 in lecture notes in math vol 996 springer verlag berlin 1983 pp 1 44 this is obtained as an application of the results in e bifet c de concini c procesi cohomology of regular embeddings adv math 82 1 1990 1 34 e strickland computing the equivariant cohomology of group compactifications math ann 291 2 1991 275 280 by a careful analysis of the relevant stanley reisner systems

non equilibrium critical behaviour on fractal lattices a simple one component surface reaction model exhibiting a critical point has been studied on deterministic fractal lattices with fractal dimension 1 df 2 results from time dependent simulations show a change in the value of the critical exponents with df two of the exponents interpolate very nicely between the values in one and two dimensions

a comparison of two reference point methods in multiple objective mathematical programming abstract when making decisions with multiple criteria a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria in multiple objective mathematical programming solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions these reference point solution methods commonly use a scalarizing function that reaches down from the ideal solution in a direction specified by the aspiration point conversely a similar scalarizing function can push out from the nadir point toward a specified aspiration point these scalarizing functions are similar in structure but diametrically opposed in their reference points in this paper we examine how these approaches behave from a technical point of view and conduct an experiment to understand better the human behaviour of users of these approaches insights we gain on the evenness of dispersion are relevant when attempting to construct a representation of the nondominated set further the technical characteristics of the two formulations solutions combined with behavioural tendencies allow us to comment on the implications for their use in interactive multiple objective methods

reformulation of gray s duality for attractive spin systems and its applications duality relations which associate two markov processes in different state spaces have been useful tools in the study of the long term behaviour of the stochastic processes of spin systems in 1986 gray introduced a new duality theory which is applicable to general spin systems with attractive transition rates the theory was developed by making full use of graphical representations in the present paper gray s duality is reformulated by studying the action of the formal generators on a newly chosen duality function and the dual processes defined in the state space upsilon a a is a finite subset of y are discussed where y is a collection of finite subsets of zd as applications of the submodularity of the survival probability sigma a of the dual processes rigorous lower bounds of the critical values are derived for the theta contact process the multi particle creation model and the sexual reproduction process

mean field approximation with coherent anomaly method for a non equilibrium model a mean field approximation for a 1d non equilibrium lattice model known as model a is considered allowing the authors to compute the probability of a configuration of a given cluster of sites the mean field equations are numerically solved in the stationary regime for different cluster sizes l or 15 from a finite size analysis and the application of the coherent anomaly method cam they compute the critical parameter of the model the correlation length critical exponent nu perpendicular to and the order parameter critical exponent beta the results are in agreement with those obtained by other methods

path integral representation for a stochastic sandpile we introduce an operator description for a stochastic sandpile model with a conserved particle density and develop a path integral representation for its evolution the resulting exact expression for the effective action highlights certain interesting features of the model for example it is nominally massless and the dynamics is via cooperative diffusion using the path integral formalism we construct a diagrammatic perturbation theory yielding a series expansion for the activity density in powers of time

perturbative series expansion for the gap of the evolution operator associated with the contact process the gap between the eigenvalues of the dominant and subdominant eigenvectors of the evolution operator associated with the contact process in one dimension is studied by perturbative series expansions in powers of the creation rate the series expansion for the gap was computed with 49 coefficients an analysis by pade approximants allowed the determination of the critical creation rate and the time correlation critical exponent

using objective values to start multiple objective linear programming algorithms we introduce in this paper a new starting mechanism for multiple objective linear programming molp algorithms this makes it possible to start an algorithm from any solution in objective space the original problem is first augmented in such a way that a given starting solution is feasible the augmentation is explicitly or implicitly controlled by one parameter during the search process which verifies the feasibility efficiency of the final solution this starting mechanism can be applied either to traditional algorithms which search the exterior of the constraint polytope or to algorithms moving through the interior of the constraints we provide recommendations on the suitability of an algorithm for the various locations of a starting point in objective space numerical considerations illustrate these ideas

generalized convexity in multiobjective programming abstract for the scalar programming problem some characterizations for optimal solutions are known in these characterizations convexity properties play a very important role in this work we study characterizations for multiobjective programming problem solutions when functions belonging to the problem are differentiable these characterizations need some conditions of convexity in differentiable scalar programming problems the concept of invexity is very important we prove that it is also necessary for the multiobjective programming problem and give some characterizations of multiobjective programming problem solutions under weaker conditions we define analogous concepts to those of stationary points and to the conditions of kuhn tucker and fritz john for the multiobjective programming problem

the reisner stanley system and equivariant cohomology for a class of wonderful varieties in this paper we are going to determine the equivariant cohomology of the wonderful compactification of a symmetric variety g h and its equivariant ring of conditions under the assumption that rk h rk g h rk g

an η approximation method in nonlinear vector optimization abstract in this paper a new approach for a solution of a nonlinear multiobjective programming problem is introduced an equivalent approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multiobjective programming problem the connection between weak efficient points in the original multiobjective programming problem and its equivalent approximated vector optimization problem is proved in this way optimality conditions for nonlinear constrained multiobjective programming problems having invex and or generalized invex objective and constraint functions with respect to the same functions are obtained

a review of interactive methods for multiobjective integer and mixed integer programming this paper makes a review of interactive methods devoted to multiobjective integer and mixed integer programming moip momip problems the basic concepts concerning the characterization of the non dominated solution set are first introduced followed by a remark about non interactive methods vs interactive methods then we focus on interactive moip momip methods including their characterization according to the type of preference information required from the decision maker the computing process used to determine non dominated solutions and the interactive protocol used to communicate with the decision maker we try to draw out some contrasts and similarities of the different types of methods

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

series analysis of the generalized contact process abstract we study critical behavior in a one parameter family of generalized contact processes using series expansions our results show that the entire family belongs to a single universality class and permit a more accurate assessment of exponent uncertainties

fock space for fermion like lattices and the linear glauber model abstract the concept of fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators a density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature some general conceptual quantities for spin lattices are then derived including the notion of generating function and path integral via grassmann variables the formalism is used to derive the liouvillian of the d dimensional linear glauber dynamics in the fock space representation then the time evolution equations for the magnetization and the two point correlation function are derived in terms of the number operator

on the critical behaviour of cellular automata models of nonequilibrium phase transitions two cellular automata models of nonequilibrium phase transitions with one adsorbing state are studied in one and two dimensions new evidence is found against the conjecture according to which all the one component models with a single adsorbing state belong to the universality class of reggeon field theory or directed percolation

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

a characterization of weakly efficient points in this paper we study a characterization of weakly efficient solutions of multiobjective optimization problems mops we find that under some quasiconvex conditions of the objective functions in a convex set of constraints weakly efficient solutions of an mop can be characterized as an optimal solution to a scalar constraint problem in which one of the objectives is optimized and the remaining objectives are set up as constraints this characterization is much less restrictive than those found in the literature up to now

a homotopy for solving polynomial systems this paper presents a continuation method for finding all solutions to polynomial systems it features a simpler homotopy than has been previously published

the balance space approach in optimization with riesz spaces valued objectives an application to financial markets the balance set approach first introduced in 1 pp 138 140 is developed for optimization problems with objective functions taking values in rn as pointed out in 2 3 balance points have important economical interpretations since the theory of riesz spaces and banach lattices become more and more the natural setting for general equilibrium and dynamic economic models see for instance 4 we propose here an extension of the balance space approach of 3 to models with objective functions taking values in riesz spaces as an application we present an optimization problem with an objective function valued in an l2 space it describes the process of an agent maximizing the profit coming from an arbitrage portfolio in a financial market

selecting subsets from the set of nondominated vectors in multiple objective linear programming in this paper we develop methods for selecting certain subsets from the set n of nondominated points for multiple objective linear programming problems one such subset is the set of a points x in n for which the maximum deviation of the objective function values c x from some ideal vector m is as small as possible this subset can be obtained as the set of nondominated points for a multiple objective problem that is considerably smaller than the original problem and the proposed method does not require that the set n be calculated explicitly the method is extended to obtain another subset of n called the trade off compromise set that has some interesting properties and that gives valuable information about possible trade offs amongst the objectives

scaling in reaction diffusion systems the authors study irreversible reaction diffusion models of the form px from k1 from mx to k2 to qx sx from k3 from nx m dc 2 n m 1 n 1 which they study for d dc using the renormalisation group in conjunction with then epsilon expansion and exact techniques for m 1 and any n the transition remains continuous they present epsilon expansions for the case n 3 by contrast for m 2 and any n the system shows a fluctuation induced first order transition

duality in nondifferentiable vector programming in this paper we study the saddle point optimality conditions and lagrange duality in multiobjective optimization for generalized subconvex like functions we obtain results which will allow us to characterize the solutions for multiobjective programming problems from the saddle point conditions and allow us to relate them to the dual problem solutions which will be adequately defined we also define a new dual problem for the multiobjective programming problem with the special property of being a scalar programming problem

use of exact penalty functions to determine efficient decisions abstract in solution methods for vector optimization problems in general substitute scalar problems are used for the determination of efficient decisions these scalar problems often contain parameters weights or levels for the objective functions whose values are to be specified by the decision maker mainly for interactive solution methods it is important to investigate which efficient decisions can be determined as solutions of the scalar problems obtained for different choices of these parameters in connection with a special scalarization our investigations show that with respect to the vector optimization problem more useful information can be obtained if the solution algorithm for the scalar problems is based on exact penalty functions

cellular automata and statistical mechanical models we elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata transient and stationary properties of probabilistic automata are linked to surface and bulk properties respectively of restricted statistical mechanical systems it is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata some exact results are derived including duality transformations exact mappings disorder and linear solutions many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties this approach is considered to be a first step toward the design of fully parallel probabilistic systems whose computational abilities rely on the cooperative behavior of their components

non equilibrium scaling in the schlogl model from the reaction diffusion master equation formulation of the schlogl model the authors develop a comprehensive description of the non equilibrium dynamics using the poisson transformation and the dynamical renormalisation group they firstly show how the equilibrium limit is recovered and secondly describe the low frequency low momenta scaling behaviour of the concentration fluctuations the approach extends simplifies or corrects previous studies and is easily generalised to treat more complicated systems

asymptotic behavior of the order parameter in a stochastic sandpile we derive the first four terms in a series for the order paramater the stationary activity density in the supercritical regime of a one dimensional stochastic sandpile in the two dimensional case the first three terms are reported this is done by reorganizing the pertubation theory derived using a path integral formalism dickman and vidigal j phys a 35 7269 2002 to obtain an expansion for stationary properties since the process has a strictly conserved particle density p the fourier mode n 1 k 0 p when n and so is not a random variable isolating this mode we obtain a new effective action leading to an expansion for in the parameter 1 1 4p this requires enumeration and numerical evaluation of more than 200 000 diagrams for which task we develop a computational algorithm predictions derived from this series are in good accord with simulation results we also discuss the nature of correlation functions and one site reduced distributions in the small high density limit