a simplified expression of the shapley function for fuzzy game abstract in this paper a simplified expression of the shapley function for games with fuzzy coalition is proposed which can be regarded as the generalization of shapley functions defined in some particular games with fuzzy coalition the simplified expression of the shapley function is compared with two definitions established by butnariu tsurumi et al a conclusion is drawn that the simplified expression of the shapley function is equivalent to butnariu s definition when characteristic function is a game with proportional values and is equivalent to tsurumi s definition when characteristic function is a game with choquet integral forms furthermore from an angle of interaction between two participation levels the properties of the two games defined by butnariu and tsurumi are respectively studied

fuzzy formulation of auctions and optimal sequencing for multiple auctions abstract current research on auctions is mainly based on the game theory in the first part of this paper we propose a fuzzy set based formulation of auctions we define fuzzy sets to represent the seller and buyers valuations bid possibilities and win possibilities analyzing the properties of these fuzzy sets we study fuzzy versions of discriminating and nondiscriminating bidding strategies for each bidder in a single object auction by using bellman and zadeh s concept of confluence of fuzzy decisions instead of the game theoretic nash equilibrium the monotonically decreasing membership function replaces of the corresponding distribution density function in milgrom and weber s auction theory in the second part of the paper we develop a soft computing approach to maximize the seller s revenue in multiple object auctions through the use of object sequencing the proposed sequencing approach is based on fuzzy rule quantification numerical experience shows the potential of the proposed approach for application in practical auctions

the consistent value of fuzzy games in the framework of fuzzy games we offer an extension of the reduced game introduced by hart and mas colell which we name the self reduced game according to consistency which related to the self reduced game we provide a definition of the consistent value which is a generalization of the shapley value of fuzzy games we adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games the first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value second based on the properties of balanced contributions and consistency we offer several axiomatizations of the consistent value finally we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments

nonlocal dispersal equations in time periodic media principal spectral theory limiting properties and long time dynamics abstract the present paper is devoted to the investigation of the following nonlocal dispersal equation u t t x d m j x y u t y d y u t x f t x u t x t 0 x where r n is a bounded and connected domain with smooth boundary m 0 2 is the cost parameter d 0 is the dispersal rate 0 characterizes the dispersal range j 1 n j is the scaled dispersal kernel and f is a time periodic nonlinear function of generalized kpp type this paper is a continuation of the works of berestycki et al 3 4 where f was assumed to be time independent we first study the principal spectral theory of the linear operator associated to the linearization of the equation at u 0 we establish an easily verifiable general and sharp sufficient condition for the existence of the principal eigenvalue as well as important sup inf characterizations of the principal eigenvalue next we study the influences of the principal spectrum point on the global dynamics and confirm that the principal spectrum point being zero is critical it is followed by the investigation of the effects of the dispersal rate d and the dispersal range characterized by on the principal spectrum point and the positive time periodic solution in particular we prove various limiting properties of the principal spectrum point and the positive time periodic solution as d 0 or to achieve these we develop new techniques to overcome fundamental difficulties caused by the lack of the usual l 2 variational formula for the principal eigenvalue the lack of the regularizing effects of the semigroup generated by the nonlocal dispersal operator and the presence of the time dependence of the nonlinearity f finally we establish the maximum principle for time periodic nonlocal dispersal operators

max min solutions for fuzzy multiobjective matrix games abstract in this paper we consider two person zero sum games with fuzzy multiple payoff matrices we assume that each player has a fuzzy goal for each of the payoffs a degree of attainment of the fuzzy goal is defined and the max min strategy with respect to the degree of attainment of the fuzzy goal is examined if all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear the formulated mathematical programming problem which yields the max min strategy can be reduced to the linear programming problem by making use of sakawa s method the variable transformations and the relaxation procedure

a banzhaf function for a fuzzy game in this paper another important solution for fuzzy games called the banzhaf function is investigated first a sim plified expression for the banzhaf function for games with fuzzy coalition is proposed the relationship between this simplified ex pression and two kinds of particular banzhaf functions are dis cussed in detail furthermore in the framework of games with fuzzy coalitions we give a definition of the potential function of fuzzy games and prove that the marginal values of the potential function are the components of the banzhaf function further more a new axiomatic characterization of the banzhaf function for games with fuzzy coalitions is provided

a direct approach to conformational dynamics based on hybrid monte carlo recently a novel concept for the computation ofessentialfeatures of the dynamics of hamiltonian systems such as molecular dynamics has been proposed the realization of this concept had been based on subdivision techniques applied to the frobenius perron operator for the dynamical system the present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework this approach allows us to define the phrase conformation in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations in a first step the frequency of conformational changes is characterized in statistical terms leading to the definition of some markov operatortthat describes the corresponding transition probabilities within the canonical ensemble in a second step a discretization oftvia specific hybrid monte carlo techniques is shown to lead to astochasticmatrixp with these theoretical preparaions an identification algorithm for conformations to be presented in a later paper is applicable it is demonstrated that the discretization oftcan be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked numerical results for the n pentane molecule and the triribonucleotide adenylyl 3 5 cytidylyl 3 5 cytidin are given and interpreted

stochastic mode reduction for the immersed boundary method we apply the formulation of a stochastic mode reduction method developed in a recent paper of majda timofeyev and vanden eijnden comm pure appl math 54 2001 pp 891 974 mtv to obtain simplified equations for the dynamics of structures immersed in a thermally fluctuating fluid at low reynolds or kubo number as simulated by a recent extension of the immersed boundary ib method by kramer and peskin proceedings of the second mit conference on computational fluid and solid mechanics elsevier science oxford uk 2003 pp 1755 1758 the effective dynamics of the immersed structures are not obvious in the primitive equations which involve both fluid and structure dynamics but the procedure of mtv allows the rigorous derivation of a reduced stochastic system for the immersed structures alone we find in the limit of small reynolds or kubo number that the lagrangian particle constituents of the immersed structures undergo a drift diffusive motion with several physically correct featur

complicated dynamics of scalar reaction diffusion equations with a nonlocal term we consider the dynamics of scalar equations ut uxx f x u c x u 0 x l where denotes some weighted spatial average and dinchlet boundary conditions are assumed prescribing f c appropriately it is shown that complicated dynamics can occur specifically linearisations at equilibria can have any number of purely imaginary eigenvalues moreover the higher order terms of the reduced vector field in an associated centre manifold can be prescribed arbitrarily up to any finite order these results are in marked contrast with the case 0 where bounded solutions are known to converge to equilibrium

steady states of a selection mutation model for an age structured population abstract we introduce a selection mutation model for an age and age at maturity structured population the age at maturity is considered an evolutionary trait on which the vital rates depend subject to selection by competition and to mutation modelled by a birth term which takes the form of a convolution like operator we prove well posedness of the initial value problem and the existence of non trivial steady states under suitable hypotheses which yield uniqueness when the interaction variable is one dimensional

a lexicographical solution concept in an n person cooperative fuzzy game abstract in this paper a new solution concept in an n person cooperative fuzzy game with sidepayment is proposed we first define an excess with respect to a player in a fuzzy game with sidepayment usually the concept of an excess is defined for each coalition in contrast however we define an excess of a player by summing up all the excess of a coalition to which he belongs by considering a payoff vector which minimizes the excess of a player in the lexicographical order we proposed a new solution concept in a fuzzy game as well as in a nonfuzzy game then we further consider the problem to extend a nonfuzzy game into a fuzzy game such an extension can be described by the mappings from a characteristic function in a nonfuzzy game into a characteristic function in a fuzzy game an illustrative numerical example of the proposed solution concept to some extended fuzzy games is also presented

blended reduced subspace algorithms for uncertainty quantification of quadratic systems with a stable mean state abstract order reduction schemes have been used successfully for the analysis and simplification of high dimensional systems exhibiting low dimensional dynamics in this work we first focus on presenting generic limitations of order reduction techniques in systems with stable mean state that exhibit irreducible high dimensional features such as non normal dynamics wide energy spectra or strong energy cascades between modes the reduced order framework that we consider to illustrate these limitations is the dynamically orthogonal do field equations this framework is applied to a series of examples with stable mean state including a linear non normal system and a nonlinear triad system in various dynamical configurations after illustrating the weaknesses and generic limitations of order reduction we develop a novel two way coupled blended approach based on the quasilinear gaussian qg closure and the do field equations the new method qg do overcomes the limitations of its two ingredients and achieves exceptional performance in the examples described previously as well as in other configurations with strongly transient character without using any tuned or adjustable parameters

a nonequilibrium statistical model of spectrally truncated burgers hopf dynamics exact spectral truncations of the unforced inviscid burgers hopf equation are hamiltonian systems with many degrees of freedom that exhibit intrinsic stochasticity and coherent scaling behavior for this reason recent studies have employed these systems as prototypes to test stochastic mode reduction strategies in the present paper the burgers hopf dynamics truncated to n fourier modes is treated by a new statistical model reduction technique and a closed system of evolution equations for the mean values of the m lowest modes is derived for m n in the reduced model the m mode macrostates are associated with trial probability densities on the phase space of the n mode microstates and a cost functional is introduced to quantify the lack of fit of paths of these densities to the liouville equation the best fit macrodynamics is obtained by minimizing the cost functional over paths and the equations governing the closure are then derived from hamilton jacobi theory the resulting reduced equations have a fractional diffusion and modified nonlinear interactions and the explicit form of both are determined up to a single closure parameter the accuracy and range of validity of this nonequilibrium closure is assessed by comparison against direct numerical simulations of statistical ensembles and the predicted behavior is found to be well represented by the reduced equations 2014 wiley periodicals inc

dynamic stochastic superresolution of sparsely observed turbulent systems real time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem the resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes which intermittently send significant energy to the large scale fluctuations hinders efficient parameterization and real time prediction using discretized pde models this issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio temporal scales and rough energy spectra near the mesh scale of numerical models here we introduce and study a suite of general dynamic stochastic superresolution dss algorithms and show that by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models one can derive stochastically superresolved velocity fields and gain insight into the important characteristics of the unresolved dynamics including the detection of the so called black swans the dss algorithms operate in fourier domain and exploit the fact that the coarse observation network aliases high wavenumber information into the resolved waveband it is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error in particular the dss algorithms are capable of successfully capturing time localized extreme events in the unresolved modes and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation moreover we show that dss improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications the skill of the various dss algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here the dss technique exploiting a simple gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade off between the superresolution skill and computational complexity associated with estimating the cross correlations between the aliasing modes of the sparsely observed turbulent signal such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse grained filtering and prediction of the next generation atmosphere ocean system aos models

parametric estimation of stationary stochastic processes under indirect observability for many natural turbulent dynamic systems observed high dimensional dynamic data can be approximated at slow time scales by a process xt driven by a systems of stochastic differential equations sdes when one tries to estimate the parameters of this unobservable sdes systems there is a clear mismatch between the available data and the sdes dynamics to be parametrized here we formalize this indirect observability framework as follows

fitting sde models to nonlinear kac zwanzig heat bath models we study a class of particle in a heat bath models which are a generalization of the well known kac zwanzig class of models but where the coupling between the distinguished particle and the n heat bath particles is through nonlinear springs the heat bath particles have random initial data drawn from an equilibrium gibbs density the primary objective is to approximate the forces exerted by the heat bath which we do not want to resolve by a stochastic process by means of the central limit theorem for gaussian processes and heuristics based on linear response theory we demonstrate conditions under which it is natural to expect that the trajectories of the distinguished particle can be weakly approximated as n by the solution of a markovian sde the quality of this approximation is verified by numerical calculations with parameters chosen according to the linear response theory alternatively the parameters of the effective equation can be chosen using time series analysis this is done and agreement with linear response theory is shown to be good

periodic p laplacian with nonlocal terms abstract in this paper we study the existence of non trivial periodic solutions for a periodic p laplacian with nonlocal terms based on the theory of leray schauder degree the key step is dealing with the degeneracy of the p laplacian and the logistic type terms arising in the right hand side of the equation

models for stochastic climate prediction there has been a recent burst of activity in the atmosphere ocean sciences community in utilizing stable linear langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory this analysis demonstrates the potential need for more sophisticated models beyond stable linear langevin equations the new phenomena include the emergence of both unstable linear langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances the strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta plane with topography and a mean flow in this example the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom

global existence and blowup of a nonlocal problem in space with free boundary abstract this paper concerns a double fronts free boundary problem for the reaction diffusion equation with a nonlocal nonlinear reaction term in space for such a problem we mainly study the blowup property and global existence of the solutions our results show that if the initial value is sufficiently large then the blowup occurs while the global fast solution exists for a sufficiently small initial data and the intermediate case with a suitably large initial data gives the existence of the global slow solution

convex fuzzy games and participation monotonic allocation schemes in this paper the cone of convex cooperative fuzzy games is studied as in the classical case of convex crisp games these games have a large core and the fuzzy shapley value is the barycenter of the core surprisingly the core and the weber set coincide as in the classical case but the coincidence of these sets for a fuzzy game does not imply automatically convexity as in the crisp case participation monotonic allocation schemes pamas are introduced and it turns out that each core element of a convex fuzzy game is pamas extendable

compactness in translation invariant banach spaces of distributions and compact multipliers abstract it is shown that for a comprehensive family of translation invariant banach spaces b b of classes of measurable functions or distributions on a locally compact group including most of the spaces of interest in harmonic analysis the following compactness criterion generalizing the well known results due to kolmogorov riesz weil concerning compact sets in lp g 1 p 0 k k g k b for all m c 0 h k g h b for all m among various applications a characterization of the space of all compact multipliers between suitable pairs of such spaces can be derived

a comparative study of two stochastic mode reduction methods abstract we present a comparative study of two methods for the reduction of the dimensionality of a system of ordinary differential equations that exhibits time scale separation both methods lead to a reduced system of stochastic differential equations the novel feature of these methods is that they allow the use in the reduced system of higher order terms in the resolved variables the first method proposed by majda timofeyev and vanden eijnden is based on an asymptotic strategy developed by kurtz the second method is a short memory approximation of the mori zwanzig projection formalism of irreversible statistical mechanics as proposed by chorin hald and kupferman we present conditions under which the reduced models arising from the two methods should have similar predictive ability we apply the two methods to test cases that satisfy these conditions the form of the reduced models and the numerical simulations show that the two methods have similar predictive ability as expected

linear fuzzy game with coalition interaction and its coincident solutions abstract in this study we consider the solution concepts for fuzzy coalition games i e cooperative games with fuzzy coalition under a certain participation level in general cooperative games with fuzzy coalition are based on the assumption that all the fuzzy coalition values for different fuzzy coalitions must be represented by the same formula which may omit the coalition interaction under different participation ratios for players considering these conditions we propose the coincident fuzziness form for games with fuzzy coalition which are represented by a mapping from the characteristic function of the crisp game to that of the fuzzy coalition game the proposed fuzzy coalition games admit the differences in coalition interactions for different fuzzy coalitions where the coalition interactions are represented by the fuzzy coalition values in different ways or formulas for a fixed fuzzy coalition the maximum fuzzy coalition game is proven to be the choquet integral form on the condition that the associate crisp game is convex in order to seek appropriate solutions for the proposed games based on a certain participation level the fuzzy shapley axioms are defined and the explicit shapley value is represented by the shapley value of the associated crisp games moreover the fuzzy core of this proposed fuzzy coalition game is the stable solution set for the given fuzzy coalition which is also denoted by the crisp cores furthermore we study the relationship between the fuzzy shapley value and the fuzzy core by adding restrictions on the fuzzy core we propose a strong fuzzy core which is a more stable solution than the fuzzy core in addition the fuzzy core is equivalent to the strong fuzzy core under some condition

a computational strategy for multiscale systems with applications to lorenz 96 model numerical schemes for systems with multiple spatio temporal scales are investigated the multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales the multiscale schemes are analyzed in general then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to lorenz issues like consistency accuracy and efficiency are discussed in detail the role of possible hidden slow variables as well as additional effects arising on the diffusive time scale are also investigated as a byproduct we obtain a rather complete characterization of the effective dynamics in lorenz model

periodic solutions of non newtonian polytropic filtration equations with nonlinear sources in this paper the authors first consider the dirichlet boundary value problem to the non newtonian polytropic filtration equation of the form u t div u m p 2 u m h x t u a in wxrwith strong nonlinear sources the existence of nontrivial periodic solutions is established based on topological degree theory the authors also studied the dirichlet boundary value problem to the equation in the form u t div u m 1u p 2 u m 1u b x t u f x t in wxrwith weak nonlinear sources the existence is treated with leray schauder fixed point theory

a mathematical framework for stochastic climate models there has been a recent burst of activity in the atmosphere ocean sciences community in utilizing stable linear langevin stochastic models for the unresolved degrees of freedom in stochastic climate prediction here a systematic mathematical strategy for stochastic climate modeling is developed and some of the new phenomena in the resulting equations for the climate variables alone are explored the new phenomena include the emergence of both unstable linear langevin stochastic models for the climate mean variables and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances all of these phenomena are derived from a systematic self consistent mathematical framework for eliminating the unresolved stochastic modes that is mathematically rigorous in a suitable asymptotic limit the theory is illustrated for general quadratically nonlinear equations where the explicit nature of the stochastic climate modeling procedure can be elucidated the feasibility of the approach is demonstrated for the truncated equations for barotropic flow with topography explicit concrete examples with the new phenomena are presented for the stochastically forced three mode interaction equations the conjecture of smith and waleffe phys fluids 11 1999 1608 1622 for stochastically forced three wave resonant equations in a suitable regime of damping and forcing is solved as a byproduct of the approach examples of idealized climate models arising from the highly inhomogeneous equilibrium statistical mechanics for geophysical flows are also utilized to demonstrate self consistency of the mathematical approach with the predictions of equilibrium statistical mechanics in particular for these examples the reduced stochastic modeling procedure for the climate variables alone is designed to reproduce both the climate mean and the energy spectrum of the climate variables c 2001 john wiley sons inc

equilibria of a predator prey model of phenotype evolution a selection mutation predator prey model for the distribution of individuals with respect to an evolutionary trait is considered existence of steady states is proved using the theory of positive semigroups we show that these steady states tend to concentrate when the mutation rate is small at the so called evolutionary stable value of the trait in the sense of adaptive dynamics of the corresponding ecological model

the nucleolus is well posed the lexicographic order is not representable by a real valued function contrary to many other orders or preorders so standard tools and results for well posed minimum problems cannot be used we prove that under suitable hypotheses it is however possible to guarantee the well posedness of a lexicographic minimum over a compact or convex set this result allows us to prove that some game theoretical solution concepts based on lexicographic order are well posed in particular this is true for the nucleolus

hamiltonian structure and statistically relevant conserved quantities for the truncated burgers hopf equation in dynamical systems with intrinsic chaos many degrees of freedom and many conserved quantities a fundamental issue is the statistical relevance of suitable subsets of these conserved quantities in appropriate regimes the galerkin truncation of the burgers hopf equation has been introduced recently as a prototype model with solutions exhibiting intrinsic stochasticity and a wide range of correlation scaling behavior that can be predicted successfully by simple scaling arguments here it is established that the truncated burgers hopf model is a hamiltonian system with hamiltonian given by the integral of the third power this additional conserved quantity beyond the energy has been ignored in previous statistical mechanics studies of this equation thus the question arises of the statistical significance of the hamiltonian beyond that of the energy first an appropriate statistical theory is developed that includes both the energy and hamiltonian then a convergent monte carlo algorithm is developed for computing equilibrium statistical distributions the probability distribution of the hamiltonian on a microcanonical energy surface is studied through the monte carlo algorithm and leads to the concept of statistically relevant and irrelevant values for the hamiltonian empirical numerical estimates and simple analysis are combined to demonstrate that the statistically relevant values of the hamiltonian have vanishingly small measure as the number of degrees of freedom increases with fixed mean energy the predictions of the theory for relevant and irrelevant values for the hamiltonian are confirmed through systematic numerical simulations for statistically relevant values of the hamiltonian these simulations show a surprising spectral tilt rather than equipartition of energy this spectral tilt is predicted and confirmed independently by monte carlo simulations based on equilibrium statistical mechanics together with a heuristic formula for the tilt on the other hand the theoretically predicted correlation scaling law is satisfied both for statistically relevant and irrelevant values of the hamiltonian with excellent accuracy the results established here for the burgers hopf model are a prototype for similar issues with significant practical importance in much more complex geophysical applications several interesting mathematical problems suggested by this study are mentioned in the final section 2002 wiley periodicals inc

population dynamics under selection and mutation long time behavior for differential equations in measure spaces abstract we study the long time behavior of solutions to a measure valued selection mutation model that we formulated in 14 we establish permanence results for the full model and we study the limiting behavior even when there is more than one strategy of a given fitness a case that arises in applications we show that for the pure selection case the solution of the dynamical system converges to a dirac measure centered at the fittest strategy class provided that the support of the initial measure contains a fittest strategy thus we term this dirac measure an asymptotically stable strategy we also show that when the strategy space is discrete the selection mutation model with small mutation has a locally asymptotically stable equilibrium that attracts all initial conditions that are positive at the fittest strategy

a note on the core minimal conversely consistent enlargement abstract the moulin reduction is extended by reducing the number of the players to the framework of fuzzy games based on this extended moulin reduction the axiomatic result of the core in tadenuma s 25 case does not hold in the context of fuzzy games and the core also violates the converse consistency therefore we propose the minimal core which possesses the converse consistency and is also the smallest solution satisfying the core

stochastic homogenization for an energy conserving multi scale toy model of the atmosphere we study a hamiltonian toy model for a lagrangian fluid parcel in the semi geostrophic limit which exhibits slow and fast dynamics we first reinject unresolved fast dynamics into the deterministic equation through a stochastic parametrization that respects the conservation of the energy of the deterministic system in a second step we use stochastic singular perturbation theory to derive an effective reduced stochastic differential equation for the slow dynamics we verify the results in numerical simulations

predictions of critical transitions with non stationary reduced order models abstract here we demonstrate the ability of stochastic reduced order models to predict the statistics of non stationary systems undergoing critical transitions first we show that the reduced order models are able to accurately predict the autocorrelation function and probability density functions pdf of higher dimensional systems with time dependent slow forcing of either the resolved or unresolved modes second we demonstrate that whether the system tips early or repeatedly jumps between the two equilibrium points flickering depends on the strength of the coupling between the resolved and unresolved modes and the time scale separation both kinds of behaviour have been found to precede critical transitions in earlier studies furthermore we demonstrate that the reduced order models are also able to predict the timing of critical transitions the skill of various proposed tipping indicators are discussed

spectral theory for general nonautonomous random dispersal evolution operators abstract we investigate the spectral theory of the following general nonautonomous evolution equation t u t x a u t x h t x u t x x d where d is a bounded subset of r n which can be a smooth domain or a discrete set a is a general linear dispersal operator for example a laplacian operator an integral operator with positive kernel or a cooperative discrete operator and h t x is a smooth function on r d we first study the influence of time dependence on the principal spectrum of dispersal equations and show that the principal lyapunov exponent of a time dependent dispersal equation is always greater than or equal to that of the time averaged one several results about the principal eigenvalue of time periodic parabolic equations are extended to general time periodic dispersal ones finally the investigation is generalized to random time dependent dispersal equations

existence of the nontrivial nonnegative periodic solutions for the quasilinear parabolic equation with nonlocal terms in this paper we study the existence of nontrivial nonnegative periodic solutions for the quasilinear parabolic equation with nonlocal terms based on the theory of leray schauder s degree

asymptotic behavior of an age structured population model and optimal maturation age abstract a continuous age structured population model with two population groups juveniles and adults and with a dynamics for the resource is considered the only density dependence is through a uniform increase of the death rates a complete description of the asymptotic behavior of the population dynamics system is obtained showing under natural hypotheses the existence of a nontrivial ecological equilibrium which attracts any initial nonzero population with nonzero initial amount of resources assuming that the offspring production rate is an increasing function of the maturation age the evolutionarily stable value of this variable is briefly discussed

normal forms for reduced stochastic climate models the systematic development of reduced low dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low frequency variability climate sensitivity and improved extended range forecasting here techniques from applied mathematics are utilized to systematically derive normal forms for reduced stochastic climate models for low frequency variables the use of a few empirical orthogonal functions eofs also known as principal component analysis karhunen loeve and proper orthogonal decomposition depending on observational data to span the low frequency subspace requires the assessment of dyad interactions besides the more familiar triads in the interaction between the low and high frequency subspaces of the dynamics it is shown below that the dyad and multiplicative triad interactions combine with the climatological linear operator interactions to simultaneously produce both strong nonlinear dissipation and correlated additive and multiplicative cam stochastic noise for a single low frequency variable the dyad interactions and climatological linear operator alone produce a normal form with cam noise from advection of the large scales by the small scales and simultaneously strong cubic damping these normal forms should prove useful for developing systematic strategies for the estimation of stochastic models from climate data as an illustrative example the one dimensional normal form is applied below to low frequency patterns such as the north atlantic oscillation nao in a climate model the results here also illustrate the short comings of a recent linear scalar cam noise model proposed elsewhere for low frequency variability

stochastic mode reduction for particle based simulation methods for complex microfluid systems we illustrate the stochastic mode reduction procedure as formulated recently by majda timofeyev and vanden eijnden comm pure appl math 54 2001 pp 891 974 mtv on the equations of motion underlying various particle based simulation approaches such as stokesian dynamics and brownian dynamics and the conceptually distinct dissipative particle dynamics dpd simulation approaches for complex microfluid systems the resulting coarse grained dynamics are compared and contrasted with each other we show that the stochastic mode reduction procedure provides a way to recover the smoluchowski dynamics for a standard model of multiple interacting particles in a fluid the dpd however has some subtle aspects which obstruct the application of the stochastic mode reduction procedure we discuss the mathematical and physical properties of the dpd method that underlie thisdifficulty

fuzzy games a characterization of the core in this paper we extend to the cooperative fuzzy games case the reduced game introduced by davis and maschler the kernel of a cooperative game naval res logist quart 12 1965 223 259 we shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency we further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse

existence of nontrivial nonnegative periodic solutions for a class of doubly degenerate parabolic equation with nonlocal terms abstract in this paper the authors establish the existence of nontrivial nonnegative periodic solutions for a class of doubly degenerate parabolic equation with nonlocal terms by using the theory of leray schauder s degree

max consistency complement consistency and the core of fuzzy games recently hwang introduced two extensions of the max reduced game to fuzzy games by reducing the number of the players based on these reduced games he offered analogous axiomatizations of the core related to serrano and volij in the context of fuzzy games here we continue and develop hwang s work on similar topics however we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels we propose such extensions of the complement reduced game and of the max reduced game to fuzzy games and define the related properties of consistency and converse consistency based on these properties we offer several analogous characterizations of the core related to peleg serrano and volij and tadenuma respectively

equations for biological evolution in this paper we consider mathematical models inspired by the mechanisms of biological evolution we take populations which are subject to interaction and mutation in the cases we consider the interaction is through competition or through a prey predator relationship the models consider the specific characteristics as taking values in real intervals and the equations are of the integro differential type in the case of competition thanks to the fact that some of the equations have solutions which are quite explicit we succeed in proving the existence of attracting stationary solutions in the case of prey and predator using techniques of dynamical systems in infinite dimensional spaces we succeed in showing the existence of a global attractor which in some instances reduces to a point our analysis takes into account having distributions corresponding to all individuals having the same characteristics as possible populations

logistic models of structured population growth abstract a general model of structured population dynamics with logistic type nonlinearity is considered the model consists of a semilinear hyperbolic partial differential equation with a linear boundary condition and an initial value the logistic nonlinearity corresponds to increased mortality as the population increases the problem is treated as an abstract semilinear evolution equation sufficient conditions are given for the solutions to converge to an equilibrium solution applications are made to age structured populations size structured populations multispecies structured populations and cell populations

adaptive sub sampling for parametric estimation of gaussian diffusions we consider a gaussian diffusion xt ornstein uhlenbeck process with drift coefficient and diffusion coefficient 2 and an approximating process y varepsilon t converging to xt in l2 as e 0 we study estimators hat gamma varepsilon hat sigma 2 varepsilon which are asymptotically equivalent to the maximum likelihood estimators of and 2 respectively we assume that the estimators are based on the available n n e observations extracted by sub sampling only from the approximating process y varepsilon t with time step e we characterize all such adaptive sub sampling schemes for which hat gamma varepsilon hat sigma 2 varepsilon are consistent and asymptotically efficient estimators of and 2 as e 0 the favorable adaptive sub sampling schemes are identified by the conditions e 0 0 e and n which implies that we sample from the process y varepsilon t with a vanishing but coarse time step e e this study highlights the necessity to sub sample at adequate rates when the observations are not generated by the underlying stochastic model whose parameters are being estimated the adequate sub sampling rates we identify seem to retain their validity in much wider contexts such as the additive triad application we briefly outline

the fuzzy core in games with fuzzy coalitions in this paper the fuzzy core of games with fuzzy coalition is proposed which can be regarded as the generalization of crisp core the fuzzy core is based on the assumption that the total worth of a fuzzy coalition will be allocated to the players whose participation rate is larger than zero the nonempty condition of the fuzzy core is given based on the fuzzy convexity three kinds of special fuzzy cores in games with fuzzy coalition are studied and the explicit fuzzy core represented by the crisp core is also given because the fuzzy shapley value had been proposed as a kind of solution for the fuzzy games the relationship between fuzzy core and the fuzzy shapley function is also shown surprisingly the relationship between fuzzy core and the fuzzy shapley value does coincide as in the classical case

cooperative fuzzy games we derive versions of known results dealing with core equilibria and shapley values of cooperative games in the case of cooperative fuzzy games i e games defined on fuzzy subsets of the set of n players a fuzzy coalition is an n vector i associating with each player i his rate of participation i 0 1 in the fuzzy coalition and the real number v is the coalition worth assumed to be positively homogeneous if also v is superadditive or equivalently concave the fuzzy game with side payments has a nonempty core associated with the coalition worth function for any ordinary game with side payments is a fuzzy extension thereof viz the fuzzy game whose coalition worth function is the least positively homogeneous superadditive function majorizing the coalition worth function of the original game the fuzzy extension always has a nonempty core moreover if the original game has a nonempty core it coincides with that of its fuzzy extension analogous results are established for games without side payments an axiomatization of values of fuzzy games with side payments is also given the results are applied to show that the set of walras equilibria coincides with the fuzzy core of an economy

on the foundations of the stochastic immersed boundary method we explore the theoretical foundations for the inclusion of thermal fluctuations in the immersed boundary method for simulating microscale fluid systems with immersed flexible structures as in cellular and subcellular biology we investigate in particular the physical validity of the thermal forcing scheme with respect to the coupling of fluid and immersed structural degrees of freedom and non equilibrium conditions we discuss also the shortcomings of a natural alternative scheme in which the thermal fluctuations are applied directly to the structural degrees of freedom through langevin type dynamics

predictability of extreme events in a nonlinear stochastic dynamical model the objective of this work is to evaluate the potential of reduced order models to reproduce the extreme event and predictability characteristics of higher dimensional dynamical systems a nonlinear toy model is used which contains key features of comprehensive climate models first we demonstrate that the systematic stochastic mode reduction strategy leads to a reduced order model with the same extreme value characteristics as the full dynamical models for a wide range of time scale separations second we find that extreme events in this model follow a generalized pareto distribution with a negative shape parameter thus extreme events are bounded in this model third we show that a precursor approach has good forecast skill for extreme events we then find that the reduced stochastic models capture the predictive skill of extreme events of the full dynamical models well consistent with previous studies we also find that the larger the extreme events the better predictable they are our results suggest that systematically derived reduced order models have the potential to be used for the modeling and statistical prediction of weather and climate related extreme events and possibly in other areas of science and engineering too

the equal allocation of nonseparable costs an extension under fuzzy behavior by considering the players and the activity levels simultaneously we propose a consistent solution which is a generalization of the equal allocation of nonseparable costs eansc on fuzzy games we also adopt two pre existing concepts from traditional game theory and reinterpret them in the framework of fuzzy games first based on the consistency which related to an extended reduced game we offer two axiomatizations of the extended eansc second by applying the excess function we propose a dynamic process to illustrate that the extended eansc can be reached by players who start from an arbitrary efficient solution and make consecutive amendments

the equalizer and the lexicographical solutions for cooperative fuzzy games characterization and properties in this paper we analyze the lexicographical solution for fuzzy tu games we study its properties and obtain a characterization the lexicographical solution was introduced by sakawa and nishizaki fuzzy sets and systems 61 1994 265 275 as a solution for crisp tu games and then extended as a value for fuzzy tu games we approach the problem by means of the close relationship that exists between the lexicographical solution for crisp tu games and the least square nucleolus a crisp value defined by ruiz et al internat j game theory 25 1996 113 134 previously and also based on this relationship we axiomatically characterize the equalizer solution for fuzzy tu games both values the equalizer and the lexicographical solutions are based on the consideration of a measure of dissatisfaction of players rather than coalitions

the general prenucleolus of n person cooperative fuzzy games abstract in this paper we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions for the general prenucleolus we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess sakawa and nishizaki 1994 15 as a result we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions such as the equalizer solution molina and tejada 2002 5 and shapley function etc we prove that the least square general prenucleolus minimizing the variance of the resulting player complaints is the general prenucleolus thus an optimal solution considered from two aspects of the lexicographic order and the least square criterion is obtained in addition several general prenucleoli are proposed in terms of specific situations

a priori tests of a stochastic mode reduction strategy several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors proc natl acad sci 96 1999 14687 commun pure appl math 54 2001 891 are developed here in this procedure reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables while the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big typically the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1 2 the examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated burgers hopf equations as a nonlinear heat bath systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables in an important illustrative example presented here the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises even for large value of the correlation time ratio of the order of 1 2 the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non gaussian statistics of the original nonlinear systems with 102 modes extremely well furthermore it is shown here that the standard regression fitting of the second order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example 2002 elsevier science b v all rights reserved

parametric estimation from approximate data non gaussian diffusions we study the problem of parameters estimation in indirect observability contexts where x t in r r is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an approximating process y varepsilon t which is close to x t in l 4 norm we construct consistent parameter estimators which are smooth functions of the sub sampled empirical mean and empirical lagged covariance matrices computed from the observable data we derive explicit optimal sub sampling schemes specifying the best paired choices of sub sampling time step and number of observations we show that these choices ensure that our parameter estimators reach optimized asymptotic l 2 convergence rates which are constant multiples of the l 4 norm y varepsilon t x t

fuzzy harsanyi solution for a kind of fuzzy coalition games abstract the fuzzy linear game in ref 32 is a class of fuzzy cooperative games with fuzzy coalition fuzzy coalition game for short which admits the difference of interactions for different fuzzy coalitions the fuzzy shapley value for fuzzy linear game has been studied as shapley value is just one point in the harsanyi solution it is interesting to study the explicit form of harsanyi solution in the fuzzy coalition game this paper defines the fuzzy harsanyi solution which distributes the harsanyi dividends such that the dividend shares of players in each fuzzy coalition are proportional to the corresponding players participation index when the fuzzy coalition payoff is average distributed between players in the fuzzy coalition the fuzzy harsanyi solution also coincides with the fuzzy shapley value just as their relationship in a crisp cooperative game we provide two axiomatic characterizations for the fuzzy harsanyi solution one uses axioms and the other uses distribution matrices the fuzzy harsanyi solution is a unique value on the fuzzy linear game that satisfies fuzzy efficiency fuzzy null player and fuzzy additivity property meanwhile based on probability distribution fuzzy harsanyi solution is seen as an expected marginal contribution of each player in the fuzzy coalition which provides more choices for players in the fuzzy coalition

reduced models of atmospheric low frequency variability parameter estimation and comparative performance abstract low frequency variability lfv of the atmosphere refers to its behavior on time scales of 10 100 days longer than the life cycle of a mid latitude cyclone but shorter than a season this behavior is still poorly understood and hard to predict the present study compares various model reduction strategies that help in deriving simplified models of lfv three distinct strategies are applied here to reduce a fairly realistic high dimensional quasi geostrophic 3 level qg3 atmospheric model to lower dimensions i an empirical dynamical method which retains only a few components in the projection of the full qg3 model equations onto a specified basis and finds the linear deterministic and the stochastic corrections empirically as in selten 1995 5 ii a purely dynamics based technique employing the stochastic mode reduction strategy of majda et al 2001 62 and iii a purely empirical multi level regression procedure which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in kravtsov et al 2005 3 the empirical dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi level regression models the extended kalman filter was used for the parameter estimation overall the reduced models perform better when more statistical information is used in the model construction thus the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full qg3 model s lfv i e its autocorrelations and spectra as well as the nonlinear properties i e the persistent flow regimes that induce non gaussian features in the model s probability density function the empirical dynamical models capture the basic statistical properties of the full model s lfv such as the variance and integral correlation time scales of the leading lfv modes as well as some of the regime behavior features but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical dynamical models but do much less well on the full qg3 model s nonlinear dynamics these results are discussed in terms of their implications for a better understanding and prediction of lfv

the principal eigenvalue for periodic nonlocal dispersal systems with time delay abstract the theory of the principal eigenvalue is established for the eigenvalue problem associated with a linear time periodic nonlocal dispersal cooperative system with time delay then we apply it to a nicholson s blowflies population model and obtain a threshold type result on its global dynamics

low dimensional chaotic dynamics versus intrinsic stochastic noise a paradigm model several prototype models are introduced here which are designed to elucidate the interaction between heteroclinic low dimensional chaos in the projected nonlinear dynamics and intrinsic stochasticity induced by energy exchange with a bath of fast variables these models are built by coupling a four dimensional ode with known analytical properties including heteroclinic cycles with a suitable deterministic bath of fast variables a systematic strategy for stochastic mode reduction is applied to these models with 104 degrees of freedom to derive four dimensional reduced stochastic equations for the slow variables due to the internal chaotic dynamics of the slow variables the stochastic mode reduction strategy is very robust in this case and yields reduced models which accurately capture the statistical behavior of the original deterministic system furthermore it is also shown here that even in the regime of a weak coupling between the slow variables and the fast heat bath the detailed structure of the stochastic terms derived through the mode elimination procedure is essential for reproducing the statistical behavior of the slow dynamics

positive periodic solutions for a system of anisotropic parabolic equations abstract we consider a system of two degenerate parabolic equations with nonlocal terms and dirichlet boundary conditions more precisely the degeneracy in each equation of the system is of the type r x laplacian where r x is a function depending on x where is a bounded smooth domain of r n the system models the diffusion and the interaction between two different biological species sharing the same territory the paper provides conditions on the parameters of the problem that guarantee the coexistence of a t periodic non negative solution u v with both non trivial u v

an ensemble kalman filter for statistical estimation of physics constrained nonlinear regression models a central issue in contemporary science is the development of nonlinear data driven statistical dynamical models for time series of noisy partial observations from nature or a complex model it has been established recently that ad hoc quadratic multi level regression models can have finite time blow up of statistical solutions and or pathological behavior of their invariant measure recently a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior here a new finite ensemble kalman filtering algorithm is developed for estimating the state the linear and nonlinear model coefficients the model and the observation noise covariances from available partial noisy observations of the state several stringent tests and applications of the method are developed here in the most complex application the perfect model has 57 degrees of freedom involving a zonal east west jet two topographic rossby waves and 54 nonlinearly interacting rossby waves the perfect model has significant non gaussian statistics in the zonal jet with blocked and unblocked regimes and a non gaussian skewed distribution due to interaction with the other 56 modes we only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation numerically we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion including the skew non gaussian distribution and autocorrelation decay on the other hand a similar stochastic model with zero memory levels fails to capture the crucial non gaussian behavior of the zonal jet from the perfect 57 mode model