基于多主体的股市模型不同市场形态下的标度行为

利用理论分析和计算机仿真相结合的方法研究一个随机多主体的股市模型,理论分析得到基础价值均衡、非基础价值均衡、周期和混沌四种市场形态的典型参数设置,基于多主体的计算机仿真产生对应参数的价格序列.对此数据的统计分析发现:股市的所有市场形态都呈现收益率分布和波动时间依赖的标度行为,其中基础价值均衡形态下收益率累积分布指数和波动时间依赖的自相似指数最大,非基础价值均衡形态下两指数最小,周期和混沌形态下居中.     

On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space

This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions,and,by using the methods of quasilinear hyperbolic systems,prove that for tree networks the natural initial,boundary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions.Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved.Finally,it is proved that,given two different equilibrium states satisfying certain conditions,it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a suffciently large time interval.     

Thermodynamic Formalism and Multifractal Analysis of Conformal Infinite Iterated Function Systems

We develop the thermodynamic formalism for equilibrium states of strongly Hölder families of functions. These equilibrium states are supported on the limit set generated by iterating a system of infinitely many contractions. The theory of these systems was laid out in an earlier paper of the last two authors. The first five sections of this paper except Section 3 are devoted to developing the thermodynamic formalism for equilibrium states of Hölder families of functions. The first three sections provide us with the tools needed to carry out the multifractal analysis for the equilibrium states mentioned above assuming that the limit set is generated by conformal contractions. The theory of infinite systems of conformal contractions is laid out in [13]. The multifractal analysis is then given in Section 7. In Section 8 we apply this theory to some examples from continued fraction systems and Apollonian packing.     

Existence,uniqueness and stability of equilibrium states for non-uniformly expanding maps

We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact metric spaces and Hölder continuous potentials with not very large oscillation. No Markov structure is assumed. If the transformation is topologically mixing there is a unique equilibrium state, it is exact and satisfies a non-uniform Gibbs property. Under mild additional assumptions we also prove that the equilibrium states vary continuously with the dynamics and the potentials (statistical stability) and are also stable under stochastic perturbations of the transformation.     

Classification of the Equilibrium States of 3He

Based on the concept of quasiaverages, we classify the equilibrium states of the superfluid ³He with due regard to possible inhomogeneous structures. We establish a relation of the residual and spatial symmetry conditions to a helicoidal ordering of the spatial anisotropy vector and a spiral structure of the magnetic anisotropy vector. We show that the set of anisotropic homogeneous equilibrium states can be classified in terms of two quantum numbers corresponding to the projections of the Cooper-pair spin and orbital momentum onto the anisotropy directions.     

Classifying magnetic and superfluid equilibrium states in magnets with the spin <Emphasis Type="Italic">s</Emphasis> = 1

Based on the method of quasiaverages, we classify magnetic and superfluid equilibrium states in magnets with the spin s = 1. Under certain simplifications, assumptions about the residual symmetry of degenerate states and the transformation properties of order parameter operators under transformations generated by additive integrals of motions lead to linear algebraic equations for a classification of the equilibrium means of the order parameters. We consider different cases of the magnetic SO(3) or SU(3) symmetry breaking and obtain solutions for the vector and tensor order parameters for particular forms of the parameters of the residual symmetry generators. We study the equilibriums of magnets with simultaneously broken phase and magnetic symmetries. We find solutions of the classification equations for superfluid equilibrium states and establish relations between the parameters of the residual symmetry generator that allow the thermodynamic coexistence of nonzero equilibrium means of the order parameters.     

ЧaПЛblГИH系统平衡状态的稳定性

考虑系统平衡状态的稳定性。给出系统的运动方程及其平衡状态的存在性条件，得到系统平衡状态的一些稳定性判据，最后举例说明其应用。     

Rates of mixing for potentials of summable variation

It is well known that for subshifts of finite type and equilibrium measures associated to Hölder potentials we have exponential decay of correlations. In this article we derive explicit rates of mixing for equilibrium states associated to more general potentials.

     

Stay-in-a-set games

There exists a Nash equilibrium (ε-Nash equilibrium) for every n-person stochastic game with a finite (countable) state space and finite action sets for the players if the payoff to each player i is one when the process of states remains in a given set of states G _i and is zero otherwise. Received: December 2000     

Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System

The multiplicity and stability of the equilibrium states of a three-dimensional differential system with initial conditions and three cross terms are studied in this paper. The existence and multiplicity of equilibrium states are given under the different qualifications of parameters. Besides, the local stability of the equilibrium state is shown by analyzing the eigenfunction of the Jacobi matrix. The global stability of the equilibrium state is obtained by constructing the Lyapunov function. Furthermore, the numerical simulation intuitively reflected the relationship of variables and verified the correctness of theoretical analysis.     

One version of the Linearized theory of nonstationary boundary-value problems with free boundary

We analyze the principle of linearization and linear boundary-value problems obtained by using this principle in the nonlinear theory of motion for a bounded volume of liquid with free surface subjected to the action of a nonstationary oscillating load. We formulate and study the problem of vibrocapillary equilibrium state, spectral problems in the theory of linear waves, and problems of stability of equilibrium states, including the problem of bifurcation of equilibrium states.     

Un Exemple de Transition de Phase

We give a new proof of the non uniqueness of the equilibrium state inF. Hofbauer's example. We extend it to obtain examples with any finite number of ergodic equilibrium states.     

Nonindependent splittings and Gibbs states

We discuss a nonindependent (beam) splitting for which the related thinning leaves the class of equilibrium states for a one mode electromagnetic field invariant. The thinning affects only the parameters of the state, showing a nonlinear loss of energy. After the splitting, the energy values of both split parts are independent. This independence is a characteristic property of the geometric distribution, the distribution of energy values in the equilibrium state. Also, we observe that the class of states where the full states of the split parts are independent is formed by the so-called phase states.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 598–605, October, 1998.This research was partially supported by the International Science Foundation under grant No. 96-0698     

Equilibrium states for non-uniformly expanding maps: Decay of correlations and strong stability

We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle–Perron–Frobenius operator acting on the space of Hölder continuous observables has a spectral gap and deduce the exponential decay of correlations and the central limit theorem. In particular, we obtain an alternative proof for the existence and uniqueness of the equilibrium states and we prove that the topological pressure varies continuously. Finally, we use the spectral properties of the transfer operators in space of differentiable observables to obtain strong stability results under deterministic and random perturbations.     

Transport of charged particles: Entropy production and Maximum Dissipation Principle

In order to describe the dynamics of crowded ions (charged particles), we use an energetic variational approach to derive a modified Poisson–Nernst–Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system has more complicated nonlinearities than the original PNP system but with the same equilibrium states. Using Galerkin's method and Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system. Different dynamics (but same equilibrium states) between the original and modified PNP systems can be represented by numerical simulations using finite element method techniques.     

Optimal control of the genital herpes epidemic

A spatial stochastic model to study the optimal control of the epidemic is introduced. The equilibrium states of the epidemic model are found. The stability and instability in linear approximation of this model are investigated. The optimal control of the unstable equilibrium states is studied. The control functions are obtained from the conditions that ensure the optimal stabilization of these states. Graphical and numerical simulation of the obtained results are presented.     

States of Infinite Equilibrium Classical Systems

We construct a measure that corresponds to the correlation functions of equilibrium states of infinite systems of classical statistical mechanics. The correlation functions satisfy the Bogolyubov compatibility conditions. We also construct measures that correspond to the correlation functions of nonequilibrium states of infinite systems for the Boltzmann hierarchy and the Bogolyubov–Strel'tsova diffusion hierarchy.     

Phase transitions in multi-phase media

Two problems on phase transitions in a continuous medium are considered. The first problem deals with an elastic medium admitting more than two phases. Necessary conditions for equilibrium states are derived. The dependence of equilibrium states on the surface tension coefficients and temperature is studied for one model of a three-phase elastic medium such that each phase has a quadratic energy density. The second problem deals with phase transitions under some restrictions on the vector field under consideration. These restrictions imply that this vector field is solenoidal and its normal component vanishes on the boundary of the interfaces of phases. The equilibrium equations are deduced. Bibliography: 5 titles. Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 120–170.     

Solution of transient markovian state probabilities and rate of approach to equilibrium states

The differential equations for transient state probabilities for Markovian processes are examined to derive the rate of convergence of transient states to equilibrium states. There is an acute need to solve the balance equations for large states, particularly for handling computer per- formance modeling with a network of queues that do not satisfy product form solutions or can- not be cast into the forms convenient for mean value analysis. The rate of convergence to equilibrium states is derived for irreducible aperiodic homogeneous Markov chains on the basis of a geometrical interpretation. A numerical integration method with dynamic step-size adjustments is applied and compared against the power method of Wallace and Rosenberg.     

Travelling waves of phase transitions in porous media

Liquid–vapour phase changes for a fluid flow through a porous medium are considered; in particular, the model allows for phase mixtures and includes an equilibrium pressure. Existence and uniqueness of travelling waves is established in a wide range of situations; the end states may be formed either by pure phases or mixtures; in the latter case the pressure equals the equilibrium pressure. A formal asymptotic analysis for vanishing relaxation time is carried out to show that the friction and reaction source terms have smoothing effect when the pressure is close to the equilibrium pressure and pure phases are avoided.