on a class of functionals invariant under a zn action abstract this document considers a system of ordinary differential equations of the form q v sub q t q f t where f and v are periodic in t v is periodic in the components of q q sub 1 q sub m and the mean value of f vanishes by showing that a corresponding functional is invariant under a natural z sub n action a simple variational argument yields at least n 1 distinct periodic solutions of more general versions of are also treated as is a class of neumann problems for semilinear elliptic partial differential equations

power law distributions and levy stable intermittent fluctuations in stochastic systems of many autocatalytic elements a generic model of stochastic autocatalytic dynamics with many degrees of freedom w i i 1 em leader n is studied using computer simulations the time evolution of the w i s combines a random multiplicative dynamics w i t 1 lambdaw i t at the individual level with a global coupling through a constraint which does not allow the w i s to fall below a lower cutoff given by cw where w is their momentary average and 0 infinity and the limit of decoupled free multiplicative random walks c 0 do not commute alpha 0 n 0 for any finite n while alpha c infinity or 1 which is the common range in empirical systems for any positive c the time evolution of w t exhibits intermittent fluctuations parametrized by a truncated levy stable distribution l alpha r with the same index alpha this nontrivial relation between the distribution of the wi s at a given time and the temporal fluctuations of their average is examined and its relevance to empirical systems is discussed

on resonant neumann problems multiplicity of solutions abstract we consider a semilinear neumann problem with an asymptotically linear reaction term we assume that resonance occurs at infinity using variational methods based on the critical point theory together with the reduction technique and morse theory we show that the problem has at least four nontrivial smooth solutions

existence and multiplicity for solutions of neumann problem for semilinear elliptic equations the existence and multiplicity results are obtained for solutions of neumann problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

sub direct sums and positivity classes of matrices abstract it is well known that a direct sum is positive semidefinite if and only if each of the direct summands is positive semidefinite in fact it is also known that this statement remains true if positive semidefinite is replaced with doubly nonnegative completely positive totally nonnegative m matrix and p matrix etc for each of these classes we consider corresponding questions for a more general sum of two matrices of which the direct sum and ordinary sum are special cases

rotation type solutions for spatially periodic hamiltonian systems along with solutions of 0 2 and in general for o l the hamiltonian h also called the energy is conserved this one dimensional situation can be studied in the phase space that is r x s since the sine function is periodic when the energy his prescribed and bigger than 1 then system 0 2 has two periodic solutions these periodic solutions however are not homotopic to a constant and they are usually called rotation type solutions it is the purpose of this paper to generalize this situation to equation 0 1 spatially periodic hamiltonian systems have been studied by several authors the nonautonomous case of 0 1 has been considered in l 7 for the existence of periodic solutions see also references therein the papers of liu s and the author 3 are specially related to this work there the existence of periodic solutions is established through a generalized saddle point theorem the hypotheses on h assumed in 3 will be considered here

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

on the periodic nonlinearity and the multiplicity of solutions abstract this document studies the multiplicity of solutions for semilinear elliptic systems as well as hamiltonian systems in which the nonlinear terms are periodic in certain variables the cuplength for cohomology rings of the torus is used our results generalize and unify several recent works by conley zehnder rabinowitz mawhin willem pucci serrin etc in particular the resonance problems and indefinite problems are studied keywords critical point neumann problem periodic solution

on the structure of the solution set of forced pendulum type equations with t periodic forcing term h with zero mean value and bounded potential g c r r has been widely studied under various assumptions on g h and t by the use of topological variational and other methods see e g 2 3 9 12 16 17 and references therein for a variety of results and techniques the main motivation for the study of p is given by physical and mechanical interpretations of the problem in this paper we are interested in existence multiplicity and properties of solutions to problem p in cases where the potential g r r and its derivative are both bounded and present an oscillating behavior in this framework the most deeply studied problem in the literature is the case in which g is a periodic function a natural and largely investigated problem of this type is given by the forced pendulum equation article no 0160

diffusion entropy analysis on the scaling behavior of financial markets abstract in this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets the scaling behaviors of four representative stock markets dow jones industrial average standardp with the scale invariance exponents all in the interval 0 92 0 95 we also estimate the local scaling exponents which indicate the financial time series is homogenous perfectly in addition a parsimonious percolation model for stock markets is proposed of which the scaling behavior agrees with the real life markets well

generalizations of the poincare birkhoff theorem in this article we prove some generalizations of the classical poincar birkhoff theorem on area preserving homeomorphisms of the annulus which satisfy a boundary twist condition the work of g d birkhoff on this theorem and its applications can be found in b1 b2 and chapter v of b3 a more modern treatment can be found in b n we prove a theorem for the open annulus a s1 x 0 1 since as we will see the theorem for the closed annulus can easily be obtained from this result for the open annulus however it is not immediately obvious what should be the analogue of the twist condition it turns out that the most general hypothesis and the most natural from the point of view of our proof involves the notion of positively and negatively returning disks for some lift of f to the covering space a r x 0 1 more precisely if f a a is a lift of f a a we will say that the e is a positively returning disk for f if there is an open disk u c a such that f u n u 0 and fp u n u k 0 forsome n k 0 here u k denotes the set x k t i x t e u thus u is disjoint from its image but under iteration by f returns to a positive translate of itself a negatively returning disk is defined similarly but with k 0 such that fl u n u 0 in section 2 we prove the following

power law distributions from additive preferential redistributions we introduce a nongrowth model that generates the power law distribution with the zipf exponent there are elements each of which is characterized by a quantity and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule while the sum of quantities is conserved the situation described by this model is similar to those of closed particle systems when conservative two body collisions are only allowed we obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model and find that the model exhibits the scaling behavior for some parameter ranges unlike well known growth models this alternative mechanism generates the power law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements this model can be applied to some examples such as personal wealths city sizes and the generation of scale free networks when only rewiring is allowed

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

the totally positive completion problem abstract an n n real matrix is said to be totally positive if every minor is non negative in this paper we are interested in totally positive completion problems that is does a partial totally positive matrix have a totally positive matrix completion this problem has in general a negative answer therefore we analyze the question for which labeled graphs g does every partial totally positive matrix whose associated graph is g have a totally positive completion when g is a path or a cycle we give necessary and sufficient conditions that guarantee the existence of the desired completion

multiple solutions of the periodic boundary value problem for some forced pendulum type equations if f x c 0 and e is a constant t then integrating 0 1 over 0 272 after multiplication of both members of the equation by x shows that the only possible solutions are constant and hence satisfy a sin x c consequently if we exclude the trivial translation by a multiple of 275 0 1 will have no solution if dj a one solution if lp a and two solutions if lc l a in 0th er t erms the intersection of the range of the operator d2 dt2 c d dt f u sin acting on zn periodic functions of class g with the subspace of constant functions in the space c o 2711 of real continuous functions on 0 27r is the closed interval a a whose interior points are images of two distinct solutions and boundary points of one we try to obtain similar results for the case where e is no more constant and

a mountain pass theorem 143 in other words the mountain separating 0 and e may even be assumed of zero altitude and the conclusion is still true moreover as we shall show if c a the critical point can be chosen with llx ll r it is interesting to ask whether this extension of the ambrosetti rabinowitz theorem remains true in the infinite dimensional case we prove here that if 1 is strengthened a little to the form 1 there exist real numbers u r r such that 0 a for every x e a x e x y a moreover if c a the critical point can be chosen with r i x0 i r roughly speaking in brief the mountain pass theorem continues to hold for a mountain of zero altitude provided it also has non zero thickness in addition if c a the pass itself occurs precisely on the mountain i e satisfying r llroll r there are two interesting and immediate corollaries the first one says that a c function which has iwo local minimum points also has a third critical point the second states that a u periodic c function with a local minimum e has a critical point x e ku k 0 1 2 the precise statements of the above results will be given in the next sec tions the proof depends upon a lemma of clark 3 formulated here in a version suitable to our purpose in section 3 some applications are presen ted for the forced pendulum equation 2

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

boolean game on scale free networks abstract inspired by the local minority game we propose a network boolean game and investigate its dynamical properties on scale free networks the system can self organize to a stable state with better performance than the random choice game although only the local information is available to each agent by introducing the heterogeneity of local interactions we find that the system will achieve the best performance when each agent s interaction frequency is linearly correlated with its information capacity generally the agents with more information gain more than those with less information while in the optimal case each agent almost has the same average profit in addition we investigate the role of irrational factor and find an interesting symmetrical behavior

power law strength degree correlation from resource allocation dynamics on weighted networks many weighted scale free networks are known to have a power law correlation between strength and degree of nodes which however has not been well explained we investigate the dynamic behavior of resource traffic flow on scale free networks the dynamical system will evolve into a kinetic equilibrium state where the strength defined by the amount of resource or traffic load is correlated with the degree in a power law form with tunable exponent the analytical results agree well with simulations

multiple solutions of neumann problem for elliptic equations abstract the multiplicity results are obtained for solutions of the neumann problem for nonlinear elliptic equations at resonance or nonresonance with unbounded nonlinearity by the reduction method and the critical point theory in particular a three critical point theorem proposed by brezis nirenberg

power law distribution of wealth in population based on a modified equiluz zimmermann model we propose a money based model for the power law distribution pld of wealth in an economically interacting population it is introduced as a modification of the equiluz and zimmermann ez model for crowding and information transmission in financial markets still it must be stressed that in the ez model a pld without exponential correction is obtained only for a particular parameter while our pattern will give the exact pld within a wide range the pld exponent depends on the model parameters in a non trivial way and is exactly calculated in this paper the numerical results are in excellent agreement with the analytic prediction and also comparable with empirical data of wealth distribution

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

periodic solutions of spatially periodic hamiltonian systems abstract this work is concerned with the study of existence and multiplicity of periodic solutions of hamiltonian systems of ordinary differential equations z j hz z t f t when the hamiltonian h z t h p q t is periodic in the variable q and superlinear in the variable p by imposing a growth condition on the derivative of h we obtain the existence of at least n 1 periodic solutions where n is the dimension of the system the existence of periodic solutions is obtained by using a saddle point theorem recently proved by lui we consider a functional over e x m where e is a hilbert space and m is a compact manifold satisfying a saddle point condition on e uniformly on m we present a proof of this saddle point theorem using standard minimax techniques based on the cup length of m

periodic solutions for nonautonomous second order systems with bounded nonlinearity some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second order systems with bounded nonlinearity by the minimax methods

subdirect sums of p p0 matrices and totally nonnegative matrices abstract in this paper the problem of when the sub direct sum of two strictly diagonally dominant p matrices is a strictly diagonally dominant p matrix is studied in particular it is shown that the subdirect sum of overlapping principal submatrices of strictly diagonally dominant p matrices is a strictly diagonally dominant p matrix it is also established that the 2 subdirect sum of two totally nonnegative matrices is a totally nonnegative matrix under some conditions it is obtained that a partial totally nonnegative matrix whose graph of the specified entries is a monotonically labeled 2 chordal graph has a totally nonnegative completion finally a positive answer to the question iv in fallat and johnson shaun m fallat c r johnson j r torregrosa a m urbano p matrix completions under weak symmetry assumptions linear algebra appl 312 2000 73 91 is given for p 0 matrices

multiple solutions of a class of neumann problem for semilinear elliptic equations abstract the multiplicity results are obtained for solutions of the neumann problem for nonlinear elliptic equations with unbounded nonlinearity by the implicit function theorem and the morse theory