an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

a coupled nonlinear system abstract a system of coupled equations is solved by the adomian decomposition method which provides an analytical approximation requiring no linearization and therefore a new approach to nonlinear problems

modification of adomian s decomposition method to solve equations containing radicals abstract adomian s decomposition method has been used in obtaining approximate solutions to a wide class of nonlinear deterministic stochastic operator equations adomian rach and sarafyan have investigated the use of the decomposition method for equations involving radicals but in such equations when the linear operator is of higher degree the direct use of adomian polynomials for the radicals produces computational difficulties while inverting the operator in particular if the initial approximation is not a constant in this paper we propose a method in which the nonlinear term in the equation involving radicals is first expanded formally in a power series the power series is then approximated by pade approximant thereby replacing the radical term by a ratio of polynomials the decomposition method of adomian is now applied to the modified equation without any difficulty as the radical type nonlinearity is now converted into a polynomial type nonlinearity

a mathematical model of adomian polynomials the adomian decomposition method is reviewed and a mathematical model of adomian polynomials is introduced to show the convenience of this model for computer programming the mathematica package is used to generate the adomian polynomials for any order

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

on the order of convergence of adomian method in this paper we contemplate the order of convergence of the decomposition method and we apply the results to some problems

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

higher order numeric wazwaz el sayed modified adomian decomposition algorithms in this paper we develop new numeric modified adomian decomposition algorithms by using the wazwaz el sayed modified decomposition recursion scheme and investigate their practicality and efficiency for several nonlinear examples we show how we can conveniently generate higher order numeric algorithms at will by this new approach including by using examples 12th order and 20th order numeric algorithms furthermore we show how we can achieve a much larger effective region of convergence using these new discrete solutions we also demonstrate the superior robustness of these numeric modified decomposition algorithms including a 4th order numeric modified decomposition algorithm over the classic 4th order runge kutta algorithm by example the efficiency of our subroutines is guaranteed by the inclusion of the fast algorithms and subroutines as published by duan for generation of the adomian polynomials to high orders

power fluctuations in stochastic models of dissipative systems we consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions actually the associated large deviation functions of the time averaged injected power required to sustain a nontrivial stationary state we discuss the results and in particular draw from our results some general features shared by these distributions in realistic dissipative systems

modulated two level system exact work statistics we consider an open two level system driven by a piecewise constant periodic field and described by a rate equation with fermi bose and arrhenius rates respectively we derive an analytical expression for the generating function and large deviation function of the work performed by the field and show that a work fluctuation theorem holds

work fluctuations in a time dependent harmonic potential rigorous results beyond the overdamped limit we investigate the stochastic motion of a brownian particle in the harmonic potential with a time dependent force constant it may describe the motion of a colloidal particle in an optical trap where the potential well is formed by a time dependent field we use the path integral formalism to solve the langevin equation and the associated fokker planck kramers equation rigorous relations are derived to generate the probability density function for the time dependent nonequilibrium work production beyond the overdamped limit we find that the work distribution exhibits an exponential tail with a power law prefactor accompanied by an interesting oscillatory feature multiple pseudo locking unlocking transitions due to the inertial effect some exactly solvable cases are discussed in the overdamped limit

a new algorithm for calculating adomian polynomials in this paper a new algorithm for calculating adomian polynomials for nonlinear operators will be established by parametrization the algorithm requires less formula than the previous method developed by adomian nonlinear stochastic operator equations academic press 1986 g adomian r rach on composite nonlinearities and decomposition method j math anal appl 113 1986 504 509 g adomian applications of nonlinear stochastic systems theory to physics kluwer 1988 many forms of nonlinearity will be studied to illustrate the new algorithm the new algorithm will be extended to calculate adomian polynomials for nonlinearity of several variables

statistics of entropy production in linearized stochastic systems we consider a wide class of linear stochastic problems driven off the equilibrium by a multiplicative asymmetric force the force breaks detailed balance maintained otherwise thus producing entropy the large deviation function of the entropy production in the system is calculated explicitly the general result is illustrated using an example of a polymer immersed in a gradient flow and subject to thermal fluctuations

energy profile fluctuations in dissipative nonequilibrium stationary states the exact large deviation function ldf for the fluctuations of the energy density field is computed for a chain of ising or more generally potts spins driven by a zero temperature dissipative glauber dynamics and sustained in a nontrivial stationary regime by an arbitrary energy injection mechanism at the boundary of the system it is found that this ldf is independent of the dynamical details of the energy injection and that the energy fluctuations unlike conservative systems in a nonequilibrium state are not spatially correlated in the stationary regime

on the adomian decomposition method and comparisons with picard s method abstract this paper shows that the adomian decomposition method stochastic systems academic press new york 1983 is not to be identified with any of the earlier methods since it solves a wide class of nonlinear and stochastic equations without the often unphysical assumptions which have become customary similarities between the picard method and the decomposition method are purely superficial

a new approach to the heat equation an application of the decomposition method abstract the author s decomposition method adomian stochastic systems academic press new york 1983 nonlinear stochastic operator equations academic press new york in press bellman and adomian partial differential equations methods for their treatment and solution reidel dordrecht 1984 adomian j comput appl math 2 1984 225 230 shown elsewhere to provide computable accurate approximate convergent solutions to nonlinear stochastic operator equations is applied to the heat equation

solutions of the initial value problem for nonlinear fractional ordinary differential equations by the rach adomian meyers modified decomposition method abstract in this paper we present the generalized adomian rach theorem and the generalized rach adomian meyers modified decomposition method for solving multi order nonlinear fractional ordinary differential equations we consider different classes of initial value problems for nonlinear fractional ordinary differential equations including the case of real valued orders and another case of rational valued orders which are solved by the present method this method can treat any analytic nonlinearity the coefficients of the solution in the form of a generalized power series are determined by a convenient recurrence scheme which does not involve integration operations compared with the classic adomian decomposition method

on linear and nonlinear integro differential equations abstract the decomposition method adomian nonlinear stochastic operator equations academic press new york in press stochastic systems academic press new york 1983 is shown to be applicable to integro differential operator equations

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

an incremental algorithm for generating all minimal models the task of generating minimal models of a knowledge base is at the computational heart of diagnosis systems like truth maintenance systems and of nonmonotonic systems like autoepistemic logic default logic and disjunctive logic programs unfortunately it is np hard in this paper we present a hierarchy of classes of knowledge bases 1 2 with the following properties first 1 is the class of all horn knowledge bases second if a knowledge base t is in k then t has at most k minimal models and all of them may be found in time o lk2 where l is the length of the knowledge base third for an arbitrary knowledge base t we can find the minimum k such that t belongs to k in time polynomial in the size of t and last where k is the class of all knowledge bases it is the case that i 1 i k that is every knowledge base belongs to some class in the hierarchy the algorithm is incremental that is it is capable of generating one model at a time

the decomposition method for nonlinear dynamical systems abstract nonlinear dynamical systems are shown to represent severe difficulties in modeling when in addition they are solved by usual perturbative or linearizing methods the mathematical solution may deviate seriously from the actual physical behavior the latter problem is significantly alleviated by use of the decomposition method of the author a number of examples are given

a large deviation analysis on the near equivalence between external and internal reservoirs within the spirit of van kampen s langevin approach we discuss the limits of validity of rephrasing the non equilibrium problem of a particle subject to an external work reservoir a system where the fluctuation dissipation relation is not verified into the simpler case with an internal heat reservoir for which the fluctuations and the dissipation arise from the same source using a convenient mapping of the thermomechanical parameters we show that counter intuitively such approach is not only valid for steady state time independent quantities but also for time dependent thermostatistical quantities namely the injected and dissipated fluxes we connect this result with the problem of large deviations and conclude that in this context we can only distinguish reservoirs by analysing the fluctuations of accumulated fluctuations as a by product we learn that the best reference approximation to the large deviation functions of a non markovian external reservoir system is not the respective internal reservoir limit as often assumed and suggested by the langevin approach but its internal reservoir analogue system obtained from the mapping of the original thermomechanical parameters

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

on the relation between default and autoepistemic logic abstract default logic is a formal means of reasoning about defaults what normally is the case in the absence of contradicting information autoepistemic logic on the other hand is meant to describe the consequences of reasoning about ignorance what must be true if a certain fact is not known although the motivation and formal character of these two systems are different a closer analysis shows that they share a common trait which is the indexical nature of certain elements in the theory in this paper we compare the expressive power of the two systems first we give an effective translation of default logic into autoepistemic logic default theories can thus be embedded into autoepistemic logic we also present a more surprising result the reverse translation is also possible so that every set of sentences in autoepistemic logic can be effectively rewritten as a default theory the formal equivalence of these two differing systems is thus established this analysis gives an interpretive semantics to default logic and yields insight into the nature of defaults in autoepistemic reasoning

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

on composite nonlinearities and the decomposition method abstract accurate convergent computable solutions using the decomposition method have been demonstrated in and papers for wide classes of nonlinear and or stochastic differential partial differential or algebraic equations it is shown specifically in this paper that composite nonlinearities of the form nx n0 n1 n2 x appearing in such equations where the ni are nonlinear operators can also be handled with the adomian an polynomials

fluctuations of power injection in randomly driven granular gases we investigate the large deviation function w for the fluctuations of the power w t wt integrated over a time t injected by a homogeneous random driving into a granular gas in the infinite time limit our analytical study starts from a generalized liouville equation and exploits a molecular chaos like assumption we obtain an equation for the generating function of the cumulants which appears as a generalization of the inelastic boltzmann equation and has a clear physical interpretation reasonable assumptions are used to obtain in a closed analytical form a legendre transform is sufficient to get the large deviation function w our main result apart from an estimate of all the cumulants of w t at large times t is that has no negative branch this immediately results in the inapplicability of the gallavotti cohen fluctuation relation gcfr that in previous studies had been suggested to be valid for injected power in driven granular gases we also present numerical results in order to discuss the finite time behavior of the fluctuations of w t we discover that their probability density function converges extremely slowly to its asymptotic scaling form the third cumulant saturates after a characteristic time larger than 50 mean free times and the higher order cumulants evolve even slower the asymptotic value is in good agreement with our theory remarkably a numerical check of the gcfr is feasible only at small times at most 10 since negative events disappear at larger times at such small times this check leads to the misleading conclusion that gcfr is satisfied for w we offer an explanation for this remarkable apparent verification in the inelastic maxwell model where a better statistics can be achieved we are able to numerically observe the failure of gcfr

on green s function in higher order stochastic differential equations abstract in adomian s solution of linear or nonlinear deterministic or stochastic differential equations the decomposition of the linear part into l r can be made so as to simplify green s function and consequently the resulting computations

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

anomalous fluctuation properties we complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by l evy noise h touchette and e g d cohen phys rev e 76 020101 r 2007 as a concrete example we consider a particle subjected to a drag force and a l evy white noise with tail index ensuremath mu 0 2 and calculate the probability distribution of the work done on the particle by the drag force as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state for 0l ensuremath mu l2 both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability for ensuremath mu 2 by contrast the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations respectively which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations the difference between these different fluctuation behaviors is discussed in the context of large deviation theory experiments that could probe or reveal an anomalous fluctuation property are also discussed

on the solution of algebraic equations by the decomposition method abstract the decomposition method g adomian stochastic systems academic press new york 1983 developed to solve nonlinear stochastic differential equations has recently been generalized to nonlinear and or stochastic partial differential equations systems of equations and delay equations and applied to diverse applications as pointed out previously see reference above the methodology is an operator method which can be used for nondifferential operators as well extension has also been made to algebraic equations involving real or complex coefficients this paper deals specifically with quadratic cubic and general higher order polynomial equations and negative or nonintegral powers and random algebraic equations further work on this general subject appears elsewhere g adomian stochastic systems ii academic press new york in press

a review of the decomposition method and some recent results for nonlinear equations abstract the decomposition method can be an effective procedure for solution of nonlinear and or stochastic continous time dynamical systems without usual restrictive assumptions this paper is intended as a convenient tutorial review of the method 1

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

nonlinear hyperbolic initial value problem the nonlinear hyperbolic equation 2u x y x y g x y f u x y 0 with u x 0 x and u 0 y y considered by hsiang and kwong j math anal appl 85 1982 31 45 under appropriate smoothness conditions is solvable by the author s decomposition method stochastic systems academic press 1983 and nonlinear stochastic operator equations academic press 1986

a rational reconstruction of nonmonotonic truth maintenance systems research note abstract the main contribution of this paper is a precise characterization of the inferences performed by nonmonotonic truth maintenance systems tmss using two standard nonmonotonic formalisms logic programming with the stable set semantics and autoepistemic logic the paper also contains an analysis of the role of dependency directed backtracking in dealing with contradictions and a proof that implementing a nonmonotonic tms is an np complete problem

adomian s method of decomposition critical review and examples of failure abstract adomian s method of decomposition is considered in application to initial boundary value problems for the one space dimensional spatially homogeneous heat conduction equation it is shown that the fundamental equation of the method is well defined only for certain restricted types of boundary conditions within the class of such boundary conditions examples are given such that the fundamental equation fails to have a unique solution and such that the sequence produced by iteration of this equation is divergent the latter is a counterexample to a published assertion of convergence

on product nonlinearities in stochastic differential equations the author s methods for solution of stochastic differential equations shown elsewhere to be applicable for nonlinear cases including polynomial exponential and trigonometric terms is shown to be applicable to product nonlinearities as well

large deviation function for entropy production in driven one dimensional systems the large deviation function for entropy production is calculated by solving a time independent eigenvalue problem for a particle driven along a periodic potential in an intermediate force regime the large deviation function shows pronounced deviations from a gaussian behavior with a characteristic kink at zero entropy production such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range

extending and implementing the stable model semantics a novel logic program like language weight constraint rules is developed for answer set programming purposes it generalizes normal logic programs by allowing weight constraints in place of literals to represent e g cardinality and resource constraints and by providing optimization capabilities a declarative semantics is developed which extends the stable model semantics of normal programs the computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics a simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised an implementation of the language the smodels system is developed based on this embedding it uses a two level architecture consisting of a front end and a kernel language implementation the front end allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules a major part of the work is the development of an efficient search procedure for computing stable models for this kernel language the procedure is compared with and empirically tested against satisfiability checkers and an implementation of the stable model semantics it offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation

default reasoning using classical logic abstract in this paper we show how propositional default theories can be characterized by classical propositional theories for each finite default theory we show a classical propositional theory such that there is a one to one correspondence between models for the latter and extensions of the former this means that computing extensions and answering queries about coherence set membership and set entailment are reducible to propositional satisfiability the general transformation is exponential but tractable for a subset which we call 2 dt a superset of network default theories and disjunction free default theories consequently coherence and set membership for the class 2 dt is np complete and set entailment is co np complete this work paves the way for the application of decades of research on efficient algorithms for the satisfiability problem to default reasoning for example since prepositional satisfiability can be regarded as a constraint satisfaction problem csp this work enables us to use csp techniques for default reasoning to illustrate this point we use the taxonomy of tractable csps to identify new tractable subsets for reiter s default logic our procedures allow also for computing stable models of extended logic programs

on the solution of nonlinear differential equations with convolution product nonlinearities abstract transform techniques can be used with differential equations containing convolution product nonlinearities to yield an algebraic equation for which the adomian polynomials are more easily obtained for solution by the decomposition method

the solution of the one dimensional nonlinear poisson s equations by the decomposition method abstract the decomposition method is a nonnumerical method for solving strongly nonlinear differential equations in this paper the method is adapted for the solution of the one dimensional nonlinear poisson s equations governing the linearly graded p n junctions in semiconductor devices and the error analysis for the approximate analytic solutions obtained by the decomposition method is carried out the simulation results show that the solutions obtained by the method are accurate and reliable and that the quantitative analysis of the linearly graded p n junctions can be conducted this work indicates that the decomposition method has some advantages which opens up a new way for the numerical analysis of semiconductor devices

a convenient computational form for the adomian polynomials abstract recent important generalizations by g adomian stochastic systems academic press 1983 have extended the scope of his decomposition method for nonlinear stochastic operator equations see also iterative method inverse operator method symmetrized method or stochastic green s function method very considerably so that they are now applicable to differential partial differential delay and coupled equations which may be strongly nonlinear and or strongly stochastic or linear or deterministic as subcases thus for equations modeling physical problems solutions are obtained rapidly easily and accurately the methodology involves an analytic parametrization in which certain polynomials an dependent on the nonlinearity are derived this paper establishes simple symmetry rules which yield adomian s polynomials quickly to high orders

a note on the decomposition method for operator equations we show for linear operator equations that adomian s decomposition method is equivalent to the classical method of successive approximations picard iterations hence in contrast to previous claims it is no more rapidly convergent than previous methods and may in fact be divergent

systems of nonlinear partial differential equations abstract the author s decomposition method 1 3 is applied to a system of nonlinear partial differential equations to demonstrate potential applicability to such systems

the decomposition method for approximate solution of the goursat problem abstract in this paper the adomian s decomposition method is effectively implemented to establish an analytic solution and a reliable numerical approximation to the goursat partial differential equation linear and nonlinear goursat examples are examined and the method supplied quantitatively reliable results for these types of problems the accuracy level of the results obtained indicates the superiority of the decomposition method over existing numerical methods that were applied to the goursat problem

modal nonmonotonic logics ranges characterization computation many nonmonotonic formalism including default logic logic programming with stable models and autoepistemic logic can be represented faithfully by means of modal nonmonotonic logics in the family proposed by mcdermott and doyle in this paper properties of logics in this family are thoroughly investigated we present several results on characterization of expansions these results are applicable to a wide class of nonmonotonic modal logics using these characterization results algorithms for computing expansions for finite theories are developed perhaps the most important finding of this paper is that the structure of the family of modal nonmonotonic logics is much simpler than that of the family of underlying modal monotonic logics namely it is often the case that different monotonic modal logics collapse to the same nonmonotonic system we exhibit four families of logics whose nonmonotonic variants coincide 5 kd45 tw5 sw5 n wk and w5 d4wb these nonmonotonic logics naturally represent logics related to commonsense reasoning and knowledge representation such as autoepistemic logic reflexive autoepistemic logic default logic and truth maintenance with negation

a new modification of the adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations abstract in this paper we propose a new modified recursion scheme for the resolution of multi order and multi point boundary value problems for nonlinear ordinary and partial differential equations by the adomian decomposition method adm our new approach including duan s convergence parameter provides a significant computational advantage by allowing for the acceleration of convergence and expansion of the interval of convergence during calculations of the solution components for nonlinear boundary value problems in particular for such cases when one of the boundary points lies outside the interval of convergence of the usual decomposition series we utilize the boundary conditions to derive an integral equation before establishing the recursion scheme for the solution components thus we can derive a modified recursion scheme without any undetermined coefficients when computing successive solution components whereas several prior recursion schemes have done so this modification also avoids solving a sequence of nonlinear algebraic equations for the undetermined coefficients fraught with multiple roots which is required to complete calculation of the solution by several prior modified recursion schemes using the adm

nonlinear stochastic differential delay equations abstract the methods used by adomian and his co workers to solve linear and nonlinear stochastic differential equations will be demonstrated to be applicable to differential equations deterministic or stochastic involving delays constant time dependent or random

the decomposition method for cauchy advection diffusion problems in this paper the solution of cauchy problems for the advection diffusion equation is obtained using the decomposition method in the case when the flow velocity is constant an analytical solution can be derived whilst for variable flow velocity symbolic numerical computations need to be performed

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

injected power fluctuations in langevin equation in this paper we consider the langevin equation from an unusual point of view that is as an archetype for a dissipative system driven out of equilibrium by an external excitation using path integral method we compute exactly the probability density function of the power averaged over a time interval of length injected and dissipated by the random force into a brownian particle driven by a langevin equation the resulting distribution as well as the associated large deviation function display strong asymmetry whose origin is explained connections with the so called fluctuation theorem are thereafter discussed finally considering langevin equations with a pinning potential we show that the large deviation function associated with the injected power is completely insensitive to the presence of a potential

global fluctuations and gumbel statistics we explain how the statistics of global observables in correlated systems can be related to extreme value problems and to gumbel statistics this relationship then naturally leads to the emergence of the generalized gumbel distribution ga x with a real index a in the study of global fluctuations to illustrate these findings we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice with local dissipation in which the fluctuations of the global energy are precisely described by the generalized gumbel distribution

solution of lanchester equation models for combat abstract this paper provides a methodology for the study of quantitative behavior of solutions to the extended system of lanchester type differential equations for the prediction of the outcome of battles under different condition the method is sufficiently general for use with nonlinear and or stochastic adaptations as well

inversion of nonlinear stochastic operators abstract the operator theoretic method adomian and malakian j math anal appl 76 1 1980 183 201 recently extended adomian s solutions of nonlinear stochastic differential equations g adomian stochastic systems analysis in applied stochastic processes nonlinear stochastic differential equations j math anal appl 55 1 1976 441 452 on the modeling and analysis of nonlinear stochastic systems in proceeding international conf on mathematical modeling vol 1 pp 29 40 to provide an efficient computational procedure for differential equations containing polynomial exponential and trigonometric nonlinear terms n y the procedure depends on the calculation of certain quantities an and bn this paper generalizes the calculation of the an and bn to much wider classes of nonlinearities of the form n y y essentially the method provides a systematic computational procedure for differential equations containing any nonlinear terms of physical significance this procedure depends on a recurrence rule from which explicit general formulae are obtained for the quantities an and bn for any order n in a convenient form this paper also demonstrates the significance of the iterative series decomposition proposed by adomian for linear stochastic operators in 1964 and developed since 1976 for nonlinear stochastic operators since both the nonlinear and stochastic behavior is quite general the results are extremely significant for applications processes need not for example be limited to either gaussian processes white noise or small fluctuations

solving nonlinear differential equations with decimal power nonlinearities abstract the decomposition method stochastic systems academic press new york 1983 nonlinear stochastic operator equations academic press new york in press is applied to the solution of nonlinear differential equations of the form ly ny x t where l is a linear differential operator and ny is a nonlinear term of the form y with a decimal number

a learning approach to the two person decentralized team problem with incomplete information a learning approach to the two person decentralized team problem with incomplete information and with a 2x2 payoff matrix is considered it is shown that if the payoff matrix is unimodal there exists a proper choice of parameters of the learning algorithm that will ensure asymptotically an expected payoff as close to maximum payoff as desired it is shown that a team problem with multimodal payoff matrix gives rise to interesting class of open problems

disjunctive stable models disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning this paper focuses on stable model semantics currently the most widely acknowledged semantics for disjunctive logic programs after presenting a new notion of unfounded sets for disjunctive logic programs we provide two declarative characterizations of stable models in terms of unfounded sets one shows that the set of stable models coincides with the family of unfounded free models i e a model is stable iff it contains no unfounded atoms the other proves that stable models can be defined equivalently by a property of their false literals as a model is stable iff the set of its false literals coincides with its greatest unfounded set we then generalize the well founded wpoperator to disjunctive logic programs give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function free programs the algorithm s soundness and completeness are proved and some complexity issues are discussed